LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

0. 


SOLENOIDS 
ELECTROMAGNETS 

AND 

ELECTEOMAGNETIC  WINDINGS 

BY 

CHARLES    R.    UNDERBILL 

CONSULTING    ELECTRICAL    ENGINEER 

ASSOCIATE    MEMBER    AMERICAN    INSTITUTE    OF    ELECTRICAL 
ENGINEERS 

223    ILLUSTRATIONS 


UNIVERSITY 

or 


NEW  YORK 

D.  VAN   NOSTRAND   COMPANY 
1910 


Engineering 

Library 


JV 


COPYRIGHT,   1910, 
BY  D.  VAN  NOSTEAND  COMPANY. 


PREFACE 

SINCE  nearly  all  of  the  phenomena  met  with  in  elec- 
trical engineering  in  connection  with  the  relations 
between  electricity  and  magnetism  are  involved  in  the 
action  of  electromagnets,  it  is  readily  recognized  that 
a  careful  study  of  this  branch  of  design  is  necessary 
in  order  to  predetermine  any  specific  action. 

With  the  rapid  development  of  remote  electrical  con- 
trol, and  kindred  electro-mechanical  devices  wherein 
the  electromagnet  is  the  basis  of  the  system,  the  want 
of  accurate  data  regarding  the  design  of  electromagnets 
has  long  been  felt. 

With  a  view  to  expanding  the  knowledge  regarding 
the  action  of  solenoids  and  electromagnets,  the  author 
made  numerous  tests  covering  a  long  period,  by  m'eans 
of  which  data  he  has  deduced  laws,  some  of  which  have 
been  published  in  the  form  of  articles  which  appeared 
in  the  technical  journals. 

In  this  volume  the  author  has  endeavored  to  describe 
the  evolution  of  the  solenoid  and  various  other  types 
of  electromagnets  in  as  perfectly  connected  a  manner 
as  possible. 

In  view  of  the  meager  data  hitherto  obtainable  it  is 
believed  that  this  book  will  be  welcomed,  not  only  by 
the  electrical  profession  in  general,  but  by  the  manu- 
facturer of  electrical  apparatus  as  well. 

iii 


iv  PREFACE 

The  thanks  of  the  author  are  due  to  Mr.  W.  D. 
Weaver,  editor  of  Electrical  World,  for  his  permission 
to  reprint  articles,  forming  the  basis  of  this  work, 
originally  published  in  that  journal,  and  also  for  his 
friendly  cooperation  and  encouragement.  The  labors 
of  Professor  Sylvanus  P.  Thompson  in  this  field  deserve 
recognition  from  the  electrical  profession,  to  which  the 
author  desires  to  add  his  personal  acknowledgments. 
The  author's  thanks  are  also  due  to  the  many  friends 
to  whose  friendship  he  is  indebted  for  the  facilities 
afforded  him  to  make  the  tests  referred  to  in  this 
volume.  To  Mr.  Townsend  Wolcott  the  author  is 
indebted  for  his  valuable  assistance  in  correcting  errors 
and  for  many  suggestions. 

CHARLES   R.   UNDERBILL. 

NEW  YORK, 
June,  1910. 


CONTENTS 


CHAPTER  I 
INTRODUCTORY 

ART.  PAGE 

1.  Definitions          .........  1 

2.  The  C.  G.  S.  System  of  Units     .         ...         .         .         .  2 

3.  General  Relations  between  Common  Systems  of  Units    .  3 

4.  Notation  in  Powers  of  Ten 7 

CHAPTER  II 
MAGNETISM  AND  PERMANENT  MAGNETS 

5.  Magnetism          .........  8 

6.  Magnetic  Field 9 

7.  Permanent  Magnets 10 

8.  Magnetic  Poles 12 

9.  Forms  of  Permanent  Magnets  ......  13 

10.  Magnetic  Induction    ........  15 

11.  Magnetic  Units 15 

CHAPTER  III 
ELECTRIC  CIRCUIT 

12.  Units 17 

13.  Circuits      . 20 

CHAPTER  IV 

ELECTROMAGNETIC  CALCULATIONS 

14.  Electromagnet!  sm      ........  24 

15.  Force  surrounding  Current  in  a  Wire        ....  24 

16.  Attraction  and  Repulsion 25 

17.  Force  due  to  Current  in  a  Circle  of  Wire  26 


vi  CONTENTS 

ART.  PAGE 

18.  Ampere-turns     .        .        .        . 27 

19.  The  Electromagnet 27 

20.  Effect  of  Permeability 28 

21.  Saturation 29 

22.  Saturation  expressed  in  Per  Cent 31 

23.  Law  of  Magnetic  Circuit   .        .        .  .        .        .32 

24.  Practical  Calculation  of  Magnetic  Circuit         ...  34 

25.  Magnetic  Leakage 36 

CHAPTER  V 
THE  SOLENOID 

26.  Definition 40 

27.  Force  due  to  Single  Turn 42 

28.  Force  due  to  Several  Turns  One  Centimeter  Apart .        .  45 

29.  Force  due  to  Several  Turns  placed  over  One  Another      .  49 

30.  Force  due  to  Several  Disks  placed  Side  by  Side        .         .  51 

31.  Force  at  Center  of  any  Winding  of  Square  Cross-section  54 

32.  Tests  of  Rim  and  Disk  Solenoids 54 

33.  Magnetic  Field  of  Practical  Solenoids      ....  61 

34.  Ratio  of  Length  to  Average  Radius          ....  65 

CHAPTER  VI 
PRACTICAL  SOLENOIDS 

35.  Tests  of  Practical  Solenoids 69 

36.  Calculation  of  Maximum  Pull  due  to  Solenoids        .         .  75 

37.  Ampere-turns  required  to  saturate  Plunger      ...  79 

38.  Relation  between  Dimensions  of  Coil  and  Plunger  .         .  82 

39.  Relation  of  Pull  to  Position  of  Plunger  in  Solenoid          .  85 

40.  Calculation  of  the  Pull  Curve 93 

41.  Pointed  or  Coned  Plungers        ......  98 

42.  Stopped  Solenoids 99 

CHAPTER  VII 
IRON-CLAD  SOLENOID 

13.   Effect  of  Iron  Return  Circuit 102 

44.   Characteristics  of  Iron -clad  Solenoids       ....  103 


CONTENTS  vii 

ART.  PAGE 

45.  Calculation  of  Pull 104 

46.  Effective  Range 105 

47.  Precautions 108 

CHAPTER  VIII 
PLUNGER  ELECTROMAGNETS 

48.  Predominating  Pull 110 

49.  Characteristics 110 

50.  Calculation  of  Pull Ill 

51.  Effect  of  Iron  Frame 112 

52.  Most  Economical  Conditions 113 

53.  Position  of  Maximum  Pull 119 

54.  Coned  Plungers 120 

55.  Test  of  a  Valve  Magnet 125 

56.  Common  Types  of  Plunger  Electromagnets      .         .        .  129 

57.  Pushing  Plunger  Electromagnet 130 

58.  Collar  on  Plunger 130 

CHAPTER  IX 
ELECTROMAGNETS  WITH  EXTERNAL  ARMATURES 

59.  Effect  of  placing  Armature  Outside  of  Winding      .        .  131 

60.  Bar  Electromagnet .         .132 

61.  Ring  Electromagnet 133 

62.  Horseshoe  Electromagnet 133 

63.  Test  of  Horseshoe  Electromagnet 134 

64.  Iron-clad  Electromagnet 136 

65.  Lifting  Magnets 137 

66.  Calculation  of  Attraction 142 

67.  Polarity  of  Electromagnets 144 

68.  Polarized  Electromagnets 144 

CHAPTER  X 
ELECTROMAGNETIC  PHENOMENA 

69.  Induction 148 

70.  Self-induction  149 


yiii  CONTENTS 

ART.  PAGE 

71.  Time-constant 150 

72.  Inductance  of  a  Solenoid  of  Any  Number  of  Layers         .  152 

73.  Eddy  Currents 153 

CHAPTER   XI 
ALTERNATING  CURRENTS 

74.  Sine  Curve 154 

75.  Pressures    .         .         .         .        .        .        .        .        .         .155 

76.  Resistance,  Reactance,  and  Impedance      ....  160 

77.  Capacity  and  Impedance 160 

78.  Resonance 161 

79.  Polyphase  Systems 164 

80.  Hysteresis 165 

CHAPTER   XII 
ALTERNATING-CURRENT  ELECTROMAGNETS 

81.  Effect  of  Inductance .         .168 

82.  Inductive  Effect  of  A.  C.  Electromagnet  ....  170 

83.  Construction  of  A.  C.  Iron-clad  Solenoids          .         .         .  171 

84.  A.  C.  Plunger  Electromagnets 172 

85.  Horseshoe  Type 174 

86.  A.  C.  Electromagnet  Calculations     .....  175 

87.  Polyphase  Electromagnets 176 

CHAPTER  XIII 

QUICK-ACTING  ELECTROMAGNETS,  AND   METHODS  OF  REDUCING 
SPARKING 

88.  Rapid  Action 184 

89.  Slow  Action 184 

90.  Methods  of  reducing  Sparking 185 

91.  Methods  of  preventing  Sticking 189 

CHAPTER   XIV 
MATERIALS,  BOBBINS,  AND  TERMINALS 

92.  Ferric  Materials 191 

93.  Annealing 192 


CONTENTS  ix 

ART.  PAGE 

94.  Hard  Rubber 192 

95.  Vulcanized  Fiber 193 

96.  Forms  of  Bobbins 194 

97.  Terminals 197 

CHAPTER   XV 
INSULATION  OF  COILS 

98.  General  Insulation 201 

99.  Internal  Insulation 201 

100.  External  Insulation 204 

CHAPTER  XVI 
MAGNET  WIRE 

101.  Material 210 

102.  Specific  Resistance 210 

103.  Manufacture 211 

104.  Stranded  Conductor 211 

105.  Notation  used  in  Calculations  for  Bare  Wires        .         .211 

106.  Weight  of  Copper  Wire 212 

107.  Relations  between  Weight,  Length,  and  Resistance        .  212 

108.  The  Determination  of  Copper  Constants          .         .         .  213 

109.  American  Wire  Gauge  (B.  &  S.) 215 

110.  Wire  Tables 215 

111.  Square  or  Rectangular  Wire  or  Ribbon  .        .        .         .217 

112.  Resistance  Wires 218 

CHAPTER  XVII 
INSULATED  WIRES 

113.  The  Insulation 220 

114.  Insulating  Materials  in  Common  Use      ....  220 

115.  Methods  of  insulating  Wires   ......  221 

116.  Temperature-resisting  Qualities  of  Insulation         .         .  222 

117.  Thickness  of  Insulation    .......  225 

118.  Notation  for  Insulated  Wires 226 

119.  Ratio  of  Conductor  to  Insulation  in  Insulated  Wires     .  227 

120.  Insulation  Thickness  228 


CONTENTS 


CHAPTER  XVIII 
ELECTROMAGNETIC  WINDINGS 

ART.  PAGE 

121.  Most  Efficient  Winding 229 

122.  Imbedding  of  Layers 232 

123.  Loss  at  Faces  of  Winding 234 

124.  Loss  Due  to  Pitch  of  Turns 234 

125.  Activity .237 

126.  Ampere-turns  and  Activity      ......  239 

127.  Watts  and  Activity 239 

128.  Volts  per  Turn 240 

129.  Volts  per  Layer 241 

130.  Activity  Equivalent  to  Conductivity        ....  242 

131.  Relations    between   Inner   and    Outer    Dimensions   of 

Winding,  and  Turns,  Ampere- turns,  etc.         .         .  245 

132.  Importance  of  High  Value  for  Activity  ....  245 

133.  Approximate  Rule  for  Resistance 246 

134.  Practical  Method  of  Calculating  Ampere-turns       .         .  246 

135.  Ampere-turns  per  Volt    .......  248 

136.  Relation  between  Watts  and  Ampere-turns    .         .         .  248 

137.  Constant  Ratio  between  Watts  and  Ampere-turns,  Volt- 

age Variable 250 

138.  Length  of  Wire 251 

139.  Resistance  calculated  from  Length  of  Wire    .        .         .  251 

140.  Resistance  calculated  from  Volume         ....  252 

141.  Resistance  calculated  from  Turns   .....  253 

142.  Exact  Diameter  of  Wire  for  Required  Ampere-turns     .  254 

143.  Weight  of  Bare  Wire  in  a  Winding         .        .         .         .254 

144.  Weight  of  Insulated  Wire  in  a  Winding         .         .         .  255 

145.  Resistance  calculated  from  Weight  of  Insulated  Wire    .  255 

146.  Diameter  of  Wire  for  a  Given  Resistance       .        .         .  256 

147.  Insulation  for  a  Given  Resistance 256 

CHAPTER  XIX 
FORMS  OF  WINDINGS  AND  SPECIAL  TYPES 

148.  Circular  Windings 257 

149.  Windings  on  Square  or  Rectangular  Cores     .         .         .  260 


CONTENTS  xi 


ART. 


150.  Windings  on  Cores  whose  Cross-sections  are  between 

Round  and  Square 263 

151.  Other  Forms  of  Windings 269 

152.  Fixed  Resistance  and  Turns 269 

153.  Tension 270 

154.  Squeezing 271 

155.  Insulated  Wire  Windings  with  Paper  between  the  Layers  272 

156.  Disk  Winding 273 

157.  Continuous  Ribbon  Winding 273 

158.  Multiple  Wire  Windings 274 

159.  Differential  Winding 274 

160.  One  Coil  wound  directly  over  the  Other          .        .        .  275 

161.  Winding  consisting  of  Two  Sizes  of  Copper  Wire  in 

Series 275 

162.  Resistance  Coils 277 

163.  Multiple-coil  Windings 277 

164.  Relation  between  One  Coil  of  Large  Diameter,  and  Two 

Coils  of  Smaller  Diameter,  Same  Amount  of  Insu- 
lated Wire,  with  Same  Diameter  and  Length  of 

Core  in  Each  Case    ....                         .  284 

165.  Different  Sizes  of  Windings  connected  in  Series     .         .  285 

166.  Series  and  Parallel  Connections 286 

167.  Winding  in  Series  with  Resistance          ....  287 

168.  Effect  of  Polarizing  Battery 294 

169.  General  Precautions 295 

CHAPTER  XX 
HEATING  OF  ELECTROMAGNETIC  WINDINGS 

170.  Heat  Units 296 

171.  Specific  Heat 0  296 

172.  Thermometer  Scales 297 

173.  Heating  Effect          .         . 298 

174.  Temperature  Coefficient 299 

175.  Heat  Tests        .                                   302 

176.  Activity  and  Heating 302 


xii  CONTENTS 

CHAPTER   XXI 
TABLES  AND  CHARTS 

PAGE 

Standard  Copper  Wire  Table 305 

Metric  Wire  Table 306 

Approximate  Equivalent  Cross-sections  of  Wires   .         .         .     307 

Bare  Copper  Wire 308 

Weight  per  Cubic  Inch  (  Wr)  for  Insulated  Wires .         .         .309 
Values  of  «j  for  Different  Thicknesses  of  Insulation        .         .     310 
Table  showing  Values  of  Na  (Turns  per  Square  Inch)  for  Dif- 
ferent Thicknesses  of  Insulation 311 

Black  Enameled  Wire 312 

Deltabeston  Wire  Table 313 

pv  Values 314-316 

Resistance  Wires 317 

Properties  of  "  Nichrome  "  Resistance  Wire  .  .  .  .318 
Properties  of  "  Climax  "  Resistance  Wire  ....  319 
Properties  of  "  Advance  "  Resistance  Wire  ....  320 

Properties  of  "  Monel  "  Wire 321 

Table  showing  the  Difference  between  Wire  Gauges       .         .     322 

Permeability  Table 323 

Traction  Table 324 

Insulating  Materials 325 

Weight  per  Unit  Length  of  Plunger  ....  326-327 
Inside  and  Outside  Diameters  of  Brass  Tubing  .  .  .  328 

Decimal  Equivalents 329 

Logarithms        .........      330-331 

Comparison  of  Magnetic  and  Electric  Circuit  Relations  .  332 
Trigonometric  Functions  .......  333 


LIST   OF  ILLUSTRATIONS 

The  Magnetic  Field Frontispiece 

FI«.  PAGE 

1.  Conversion  Chart.     Linear 4 

2.  Conversion  Chart.     Area  and  Volume      ....  5 

3.  Conversion  Chart.     Weights     ......  6 

4.  Closed  Ring  Magnet  ........  9 

5.  Separated  King  Magnet     .......  10 

6.  Field  of  Force  surrounding  Magnet 11 

7.  Bar  Permanent  Magnet 14 

8.  Horseshoe  Permanent  Magnet  ......  14 

9.  Magnet  with  Consequent  Poles 14 

10.  Compound  Magnet 15 

11.  Resistances  in  Series           .......  20 

12.  Resistances  in  Multiple 20 

13.  Divided  Circuit  in  Series  with  Resistance         .         .         .21 

14.  Relation  between  Directions  of  Current  and  Force  sur- 

rounding It 24 

15.  Distortion  of  Field  due  to  Circular  Current      ...  26 

16.  Strength  of  Field  at  Varying  Distances  from  Center  of 

Loop 27 

17.  Permeability  Curve 29 

18.  Magnetization  Curve 30 

19.  Saturation  Curve  plotted  to  Different  Horizontal  Scales  .  31 

20.  Ampere-turns  per  Unit  Length  of  Magnetic  Circuit         .  35 

21.  Absence  of  External  Field         . 36 

22.  Leakage  Paths    . 37 

23.  Leakage  Paths  around  Air-gap           .....  37 

24.  Reluctance  between  Cylinders  ......  39 

25.  Sixteen-turn  Coil 40 

26.  One-turn  Coil 40 

27.  Simple  Solenoid 41 

28.  Force  due  to  Turns  of  Different  Radii       ....  43 

29.  Sums  of  Forces  for  Various  Radii  of  Turns      ...  48 

xiii 


xiv  LIST  OF  ILLUSTRATIONS 

FIG.  PAGE 

30.  Group  of  Turns  placed  over  One  Another         ...  49 

31.  Groups  of  Turns  arranged  to  form  a  Large  Square  Group  51 

32.  The  Test  Solenoids 54 

33.  Dimensions  of  Rim  Solenoids 55 

34.  Dimensions  of  Disk  Solenoids 56 

35.  Method  of  Testing  Rim  and  Disk  Solenoids     ...  57 

36.  Characteristics  of  Rim  Solenoids 58 

37.  Characteristics  of  Disk  Solenoids      .....  59 

38.  Ratio  of  rm  to  Pull  for  Rim  and  Disk  Solenoids       .         .  60 

39.  Rim  Solenoids  telescoped  to  form  Disk  Solenoid      .         .  61 

40.  Product  of  Pull  and  Mean  Magnetic  Radius     ...  62 

41.  Plunger  removed  from  Solenoid 63 

42.  Plunger  inserted  One-third  into  Solenoid          ...  63 

43.  Plunger  inserted  Two-thirds  into  Solenoid       ...  64 

44.  Plunger  entirely  within  the  Solenoid        ....  64 

45.  Force  due  to  Solenoids  with  Unit  Thickness  or  Depth  of 

Winding 66 

46.  Effect  of  Changing  Thickness  of  Winding        ...  67 

47.  Testing  Apparatus 69 

48.  Maximum  Pulls  due  to  Practical  Solenoids  of  Various 

Dimensions 71 

49.  Effect  of  varying  Position  of  Plunger  in  Solenoid    .         .  72 

50.  Effect  due  to  varying  Position  of  Plunger  in  Solenoid      .  73 

51.  Solenoid  Core  consisting  of  One  Half  Air,  and  One  Half 

Iron 77 

52.  Approximate  Ampere-turns  required  to  saturate  Plunger  80 

53.  Characteristic  Force  Curves  of  Solenoid    ....  81 

54.  Ratio  between  Ampere-turns  and  Cross-sectional  Area  of 

Plunger 84 

55.  Characteristics  of  Solenoid  15.3  cm.  Long         ...  86 

56.  Characteristics  of  Solenoid  22.8  cm.  Long         ...  87 

57.  Characteristics  of  Solenoid  30.5  cm.  Long         ...  87 

58.  Characteristics  of  Solenoid  45.8  cm.  Long         ...  86 

59.  Characteristics  of  45.8  cm.-Solenoid  with  Plunger  of  the 

Same  Length 88 

60.  Characteristics  of  Solenoid  25.4  cm.  Long         ...  89 

61.  Characteristics  of  Solenoid  8  cm.  Long     ....  90 

62.  Characteristics  of  Solenoid  15  cm.  Long   ....  91 

63.  Characteristics  of  Solenoid  17.8  cm.  Long         ...  91 


LIST   OF  ILLUSTRATIONS  xv 

FIG.  PAGE 

64.  Effect  of  Increased  m.  m.f.  on  Range  of  Solenoid    .        .  92 

65.  Comparison  of  Solenoids  of  Constant  Radii,  but  of  Dif- 

ferent Lengths 93 

66.  Curves  in  Fig.  65  reduced  to  a  Common  Scale  ...  94 

67.  Average  of  Curves 96 

68.  Average  Solenoid  Curve  compared  with  Sinusoid    .         .  96 

69.  Effect  of  increasing  Ampere-turns 97 

70.  Experimental  Solenoid 99 

71.  Characteristics  of  Experimental  Solenoid          .         .        .  100 

72.  Iron -clad  Solenoid 102 

73.  Characteristics  of  Simple  and  Iron-clad  Solenoids    .         .  103 

74.  Magnetic  Cushion  Type  of  Iron-clad  Solenoid  .         .         .103 

75.  Characteristics  of  Iron-clad  Solenoid.     L  -  4.6          .         .  105 

76.  Characteristics  of  Iron-clad  Solenoid.     L  =  8.0         .        .  106 

77.  Characteristics  of  Iron-clad  Solenoid.     L  =  11.4       .         .  106 

78.  Characteristics  of  Iron-clad  Solenoid.     L  —  15.2        .         .  107 

79.  Characteristics  of  Iron-clad  Solenoid.     L  =  17.8       .        .  107 

80.  Plunger  Electromagnet 110 

81.  Characteristics  of  Plunger  Electromagnet         .         .         .  Ill 

82.  Method  of  determining  Proper  Flux  Density   .         .         .114 

83.  8£&  Curves  for  Iron  and  Air-gap 116 

84.  Air-gaps  for  Maximum  Efficiency 118 

85.  Test  showing  Position  of  Air-gap  for  Maximum  Pull      .  119 

86.  Flat-faced  Plunger  and  Stop 120 

87.  Coned  Plunger  and  Stop 121 

88.  Comparison  of  Dimensions  and  Travel  of  Flat-faced  and 

Coned  Plungers  and  Stops 122 

89.  Flux  Paths  between  Coned  Plunger  and  Stop  .         .         .123 

90.  Effect  of  changing  Angles          ......  124 

91.  Design    of   a   Tractive   Electromagnet  to  perform   400 

cm.-kgs.  of  Work 125 

92.  Valve  Magnet 126 

93.  Characteristics  of  Valve  Magnet 127 

94.  Characteristics  of  Valve  Magnet 128 

95.  Horizontal  Type  of  Plunger  Electromagnet      .         .         .  129 

96.  Horizontal  Type  of  Plunger  Electromagnet      .         .         .129 

97.  Vertical  Type  of  Plunger  Electromagnet          .         .         .129 

98.  Two-coil  Plunger  Electromagnet 129 

99.  Pushing  Plunger  Electromagnet 130 


xvi  LIST  OF   ILLUSTRATIONS 


100.  Electromagnet  with  Collar  on  Plunger    ....  130 

101.  Characteristics  of  Test  Magnet        .....  131 

102.  Test  Magnet 132 

103.  Bar  Electromagnet 132 

104.  Electromagnet  with  Winding  on  Yoke   ....  132 

105.  Horseshoe  Electromagnet 133 

106.  Practical  Horseshoe  Electromagnet          ....  133 

107.  Modified  Form  of  Horseshoe  Electromagnet  .         .         .  134 

108.  Experimental  Electromagnet 134 

109.  Characteristics  of  Horseshoe  Electromagnet  .         .         .  135 

110.  Relation  of  Work  to  Length  of  Air-gap  .         .         .         .135 

111.  Iron-clad  Electromagnet 136 

112.  Skull-cracker 138 

113.  Lifting  Magnet 139 

114.  Plate  and  Billet  Magnet 140 

115.  Ingot  Magnet 141 

116.  Method  of  increasing  Attracting  Area    ....  143 

117.  Electromagnet  with  Flat-faced  and  Rounded  Core  Ends  143 

118.  Polarized  Striker  Electromagnet 145 

119.  Polarized  Relay 145 

120.  Polarized  Electromagnet  ......  146 

121.  Polarized  Electromagnet 146 

122.  Polarized  Electromagnet 147 

123.  Production  of  Alternating  Currents         ....  154 

124.  Relative  Angular  Positions  of  Conductor        .        .        .  154 

125.  Sinusoid 155 

126.  Impressed  e.  m.f.  Balancing  (nearly)  e.  in.  f.  of   Self- 

induction  .........  157 

127.  Phase  Relations  when  Ea  =  E8       .        .        .        .        ,158 

128.  Condenser 160 

129.  Conditions  for  Resonance 162 

130.  Effects  of  Resonance 163 

131.  Two-phase  Currents .164 

132.  Three-phase  Currents 164 

133.  Two-phase  System 165 

134.  Star  or  Y  Connection,  Three-phase          •        .        .        .165 

135.  Delta  Connection,  Three-phase 165 

136.  Hysteresis  Loop        .        . 167 

137.  A.C.  Solenoid  .                                  168 


LIST  OF  ILLUSTRATIONS  xvii 

FTO.  PAGE 

138.   Characteristics  of  A.  C.  Solenoid 168 

130.    Inductance  Coil  with  Taps 169 

140.  Characteristics  of  Inductance  Coil  with  Taps          .         .  169 

141.  Effect  due  to  varying  Iron  in  Core  .         .         .         .         .170 

142.  Method  of  eliminating  Noise  in  A.  C.  Iron-clad  Solenoid  171 

143.  Laminated  Core 172 

144.  A.  C.  Plunger  Electromagnet 172 

145.  Two-coil  A.  C.  Plunger  Electromagnet    ....  172 

146.  Characteristics  of  Two-coil  A.  C.  Plunger  Electromagnet  173 

147.  A.  C.  Horseshoe  Electromagnet       .....  175 

148.  Single-phase  Magnets  on  Three-phase  Circuit         .         .  177 

149.  Polyphase  Electromagnet 177 

150.  Connections  of  Coils  of  Polyphase  Electromagnet  .         .177 

151.  Two-phase    Electromagnet    supplied    with    Two-phase 

Current 178 

152.  Two-phase   Electromagnet  supplied  with   Three-phase 

Current ...  179 

153.  Test   of   Two-phase   Electromagnet  with    Three-phase 

Current 180 

154.  Connection  Diagram  for  Polyphase  Electromagnet  on 

Single-phase  Circuit 182 

155.  Phase  Relations  in  Polyphase  Electromagnet  on  Single- 

phase  Circuit 182 

156.  Retardation  Test  of  Direct-current  Electromagnet          .  185 

157.  Resistance  and  e.m.f.  in  Series  in  Shunt  with  "Break"  187 

158.  Differential  Method 188 

159.  Bobbin  with  Iron  Core 195 

160.  Terminal  Conductor 198 

161.  Terminal  Conductor  with  Water  Shield          .         .         .199 

162.  Method  of  bringing  out  Terminal  Wires         .         .        .199 

163.  Method  of  bringing  out  Terminal  Wires         .         .        .  200 

164.  Method  of  bringing  out  Terminal  Wires         .         .         .  200 

165.  Methods  of  tying  Inner  and  Outer  Terminal  Wires       .  200 

166.  Sectional  Winding 201 

167.  Insulation  between  Layers       ......  201 

168.  Method  of  mounting  Fringed  Insulation         .         .         .  205 

169.  Insulation  of  Bobbins 206 

170.  Insulation  of  Bobbins 206 

171.  Test  of  Magnet  Wire 223 


xviii  LIST  OF  ILLUSTRATIONS 

FIG.  PAGE 

172.  Space  Utilization  of  Round  Wire 230 

173.  Space  Utilization  of  Square  Wire 230 

174.  Space  Utilization  of  Imbedded  Wires     ....  232 

175.  Relations  of  Imbedded  Wires 232 

176.  Test  of  an  8-layer  Magnet  Winding        .        .         .         .233 

177.  Loss  of  Space  by  Change  of  Plane  of  Winding       .        .  234 

178.  Ideal  Turn 235 

179.  Pitch  when  di  =  M 236 

180.  Effects  due  to  Pitch  of  Winding 237 

181.  Weight  of  Copper  in  Insulated  Wires     ....  238 

182.  Showing  where  the  Greatest  Difference  of  Potential 

Occurs 241 

183.  Loss  of  Space  by  Insulation  on  Wires     ....  242 

184.  Characteristics  of   Winding  of   Constant    Turns    and 

Length  of  Wire 243 

185.  Characteristics  of  Winding  of  Constant  Resistance        .  243 

186.  Characteristics  of  Winding  of  Constant  Cross-section 

of  Wire 244 

187.  Effect  upon  Characteristics  of  Windings  of  varying  the 

Perimeters 245 

188.  Ampere-turn  Chart 247 

189.  Chart   showing   Ratio  between   Watts   and   Ampere- 

turns          249 

190.  Winding  Dimensions 257 

191.  Chart  for  Determining  Winding  Volume        .        .        .259 

192.  Imaginary  Square-core  Winding 260 

193.  Practical  Square-core  Winding 260 

194.  Winding  on  Core  between  Square  and  Round        .        .  261 

195.  Round-core  Winding 263 

196.  Ratios  between  Outside  Dimension  B  of  Square-core 

Electromagnets,  and  Outside  Diameter  of  Round- 
core  Electromagnets 264 

197.  Ratios  between  Round-core   and   Square-core   Electro- 

magnets when  -  =  0 266 

a 

198.  Ratios  between  Square-core  and  Round-core  Electro- 

T 

magnets  when  —  =  2 266 

a 


LIST  OF  ILLUSTRATIONS  xix 

FIG.  PAGE 

199.  Maximum  Values  for  Flux  Density  and  Total  Flux, 

and  Ratios  between  Core  Area  and  Average  Perim- 
eters    267 

200.  Maximum  Flux  Density  and  Total  Flux,  for  Various 

Values  of  —  and  -       .  268 
a             a 

201.  Four-wire  Winding 274 

202.  Winding  with  Layers  Connected  in  Multiple           .         .  278 

203.  Practical  Multiple-coil  Winding 279 

204.  Method  of  bringing  out  Terminals           ....  279 

205.  Bobbin 280 

206.  Mean  Diameters  of  Multiple-coil  Windings    .         .         .  281 

207.  Characteristics  of  Two  Resistances  in  Series  .         .         .  288 

208.  Effect  with  Variable  Thickness  of  Insulation,  —  Con- 

rfja 

stant  .                290 

209.  Effect  of  Insulation 291 

210.  Effect  with    Constant    Thickness    of    Insulation,    — 

d* 

Variable 292 

211.  Curve  «e"  as  a  Straight  Line 293 

212.  Comparison  of  Thermometer  Scales         ....  297 

213.  Temperature  Coefficients 300 

214.  Heat  Test 301 

215.  Weight  per  Cubic  Inch  (  Wv)  for  Insulated  Wires          .  309 

216.  pv  Values.     Nos.  10  to  16  B.  &  S 314 

217.  pv  Values.     Nos.  16  to  21  B.  &  S 314 

218.  pv  Values.     Nos.  21  to  26  B.  &  S 315 

219.  pv  Values.     Nos.  26  to  31  B.  &  S 315 

220.  pv  Values.    Nos.  31  to  36  B.  &  S 316 

221.  pi  Values.     Nos.  36  to  40  B.  &  S 316 

222.  Weight  per  Unit  Length  of  Plunger        .         .         .         .326 

223.  Weight  per  Unit  Length  of  Plunger        ....  327 


SOLENOIDS,  ELECTROMAGNETS,  AND 
ELECTROMAGNETIC   WINDINGS 

CHAPTER   I 
INTRODUCTORY 

1.    DEFINITIONS 

Force  is  that  which  produces  or  tends  to  produce 
motion. 

Resistance  is  whatever  opposes  the  action  of  a  force. 

Work  is  the  overcoming  of  resistance  continually 
occurring  along  the  path  of  motion. 

Energy  is  the  capacity  for  doing  work  ;  therefore, 
the  amount  of  work  that  may  be  done  depends  upon 
the  amount  of  energy  expended. 

The  Effective  Work  is  the  actual  work  accomplished 
after  overcoming  friction. 

Time  is  the  measure  of  duration. 

Power  is  the  rate  of  doing  work,  and  is  equal  to  work 
divided  by  time. 

It  is  to  be  noted  that  work  does  not  embrace  the  time 
factor ;  that  is,  no  matter  whether  a  certain  amount  of 
work  requires  one  minute  or  one  month  to  accomplish, 
the  value  of  work  will  be  the  same. 

With  power,  however,  time  is  an  important  factor; 
for,  if  a  certain  amount  of  work  is  to  be  accomplished 

l 


2  SOLENOIDS 

by  one  machine  in  one  half  the  time  required  by  an- 
other, the  former  will  require  twice  the  power  required 
in  the  latter. 

The  product  of  power  into  time  equals  the  amount  of 
work. 

Efficiency  is  the  ratio  between  the  effective  work  and 
the  total  energy  expended.  It  is  usually  expressed  as 
a  percentage. 

2.   THE  C.  G.  S.  SYSTEM  OP  UNITS 

The  Centimeter-  Grram-Second  system  embraces  the 
Centimeter  as  the  unit  of  length,  the  Grram  as  the  unit 
of  mass,  and  the  Second  as  the  unit  of  time.  These  are 
the  Fundamental  units. 

The    centimeter    is    0.01    Meter,   the    meter   being 

part    of   the    earth-quadrant   through   the 

10,000,000    F 

meridian  of  Paris,  measured  from  the  Equator  to  the 
North  Pole.  The  equivalent  of  the  meter  is,  in  English 
measure,  39.37  inches.  Therefore,  1  centimeter  = 
0.3937  inch. 

The  G-ram  is  equal  to  one  cubic  centimeter  of  dis- 
tilled water  at  its  maximum  density,  which  is  at  4° 
Centigrade.  Mass  is  a  constant,  but  weight  varies  at 
different  places  according  to  the  force  of  gravitation  at 
those  places.  The  equivalent  of  the  gram  in  English 
measure  is  0.00220464  pound. 

The  Second  is  the     ^    ^  part  of  the  mean  solar  day. 

8b,400 

The  Absolute  units  are  based  upon  the  fundamental 
units. 

The  Dyne  is  the  absolute  unit  of  force,  and  is  that 
force  which,  acting  upon  one  gram  for  one  second, 


INTRODUCTORY  3 

imparts  to  it  a  velocity  of  one  centimeter  per  second. 
The  pull  due  to  gravity  on  1  gram  =  981  dynes. 

The   Erg  is  the  absolute  unit  of  work,  and  is  the 
work  done  when  one  dyne  acts  through  one  centimeter. 
The  following  prefixes  are  used  in  the  C.  G.  S.  system. 
Mili  meaning  thousandth  part. 
Centi  meaning  hundredth  part. 
Deci  meaning  tenth  part. 
Deca  meaning  ten. 
Hecto  meaning  one  hundred. 
Kilo  meaning  one  thousand. 

Thus  the  centimeter  is  the  one  hundredth  part  of  the 
meter ;  the  kilometer  is  one  thousand  meters,  etc. 

Abbreviations  for  the  metric  units  are  m.  for  meter, 
cm.  for  centimeter,  mm.  for  milimeter,  g.  for  gram,  kg. 
for  kilogram,  etc. 

3.    GENERAL  RELATIONS  BETWEEN  COMMON 

SYSTEMS  OF  UNITS 

In  the  English  system  of  units  the  mechanical  unit 
of  work  is  the  Foot-pound,  and  is  the  amount  of  work 
required  to  raise  one  pound  vertically  one  foot. 

The  mechanical  unit  of  power  is  the  Horse-power,  and 
is  the  power  required  to  raise  33,000  pounds  one  foot 
vertically,  in  one  minute,  or,  in  other  words,  33,000  foot- 
pounds per  minute. 

Since  the  laws  of  electrical  engineering  are  expressed 
in  terms  of  the  C.  G.  S.  units,  these  units  should  be  used 
as  much  as  possible  in  all  calculations. 

Figures  1  to  3  show  the  relations  between  the  Eng- 
lish and  C.  G.  S.  units  most  commonly  used. 

In  general  it  may  be  stated  that  the  calculations  of 
the  magnetic  circuit  may  be  made  in  metric  units,  while 


SOLENOIDS 


¥                  J 

INCH 
1             1              1             I             1              / 

99 

0 

1 

o 

a. 

o 

3 

0. 

4 

0 

S 

O 

G 

0 

7 

O 

6 

0 

a 

' 

x 

/ 

80 
70 
60 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

9O 

/ 

/ 

/ 

/ 

/ 

/ 

/O 

/ 

/ 

/ 

/ 

/= 

££7 

' 

\ 

A5 


1.0 


0.5 


O        A,      +      6      Q      tO     u     ft     /6     /a    20    22     24-   26    2&    3O    3Z    3*    36    38 

FIG.  1.  —  Conversion  Chart.    Linear. 


INTRODUCTORY 


\ 
/.o 

0.9 
0.8 

CUBI 
>          ±           4           6           ( 

C    CEMTIMBTERS 
?          /o         12          14         16^ 

/s 

2*/n 

/ 

/ 

03 

0.8 
0.7 

03 

o./ 
o 

3 

i 

j 

/ 

/ 

/ 

/ 

/ 

i 

/ 

/ 

/ 

66 
05 

0.4 
03 

o-z 
o./ 

o 

/ 

/ 

' 

<s 

\ 

'/ 

i 

y 

7 

/ 

i 

/ 

/ 

/ 

/ 

' 

/ 

x 

/ 

/ 

/ 

/ 

/ 

/ 

y 

// 

/, 

/ 

a 

/ 

l__ 

/          4          3         4          5         *          ?         9         9         / 

SQUARE    CE#T/M£T£K$ 

FIG.  2.  —  Conversion  Chart.    Area  and  Volume. 


SOLENOIDS 


SCO 


FIG.  3.  —  Conversion  Chart.    Weights. 


INTRODUCTORY  7 

it  may  be  more  convenient  to  express  the  dimensions 
of  the  winding,  diameter  of  wire  and  thickness  of 
insulation  by  English  units,  since  nearly  all  obtainable 
data  for  insulated  wires  are  given  in  the  latter  units. 
However,  the  formulae  in  this  book  are  so  arranged 
that  either  system  may  be  used.  By  the  use  of  the 
charts  in  Figs.  1  to  3  conversions  may  be  easily  made. 

4.   NOTATION  IN  POWERS  OF  TEN 

Instead  of  writing  a  number  like  ten  millions  thus : 
10,000,000,  it  is  often  more  convenient  to  express  it 
thus:  107.  Therefore,  the  number  2,140,000  maybe 
written  214  x  104,  or  2.14  x  106. 

Likewise,  —  may  be  expressed   10"1,  and 


10       '  1,000,000' 

10~6,  etc. 


CHAPTER   II 
MAGNETISM  AND  PERMANENT  MAGNETS 

5.   MAGNETISM 

'•''Magnetism  is  that  peculiar  property  occasionally 
possessed  by  certain  bodies  (more  especially  iron  and 
steel)  whereby  under  certain  circumstances  they  natu- 
rally attract  or  repel  one  another  according  to  deter- 
minate laws." 

The  ancients  in  Magnesia,  Thessaly,  are  supposed  to 

have  been  the  original  discoverers  of  magnetism,  where 

an  ore  possessing  a  remarkable  tractive  power  for  iron 

was  found.     To  a  piece  of  this  iron-attracting  ore  was 

1  given  the  name  Magnet. 

It  was  further  found  that  a  piece  of  this  ore,  when 
freely  suspended,  swung  into  such  a  position  that  its 
ends  pointed  north  and  south,  which  discovery  made  it 
possible  for  navigators  to  steer  their  ships  by  means  of 
the  Lodestone  (leading  stone). 

A  piece  of  hardened  steel  was  found  to  possess  the 
properties  of  the  lodestone  when  the  former  was  rubbed 
by  the  latter  ;  thus  becoming  an  Artificial  Magnet. 

There  is  no  known  insulator  of  magnetism;  nearly 
all  substances  have  the  same  conducting  power  as  air, 
which,  however,  is  not  a  very  good  conductor.  A 
magnetic  substance  is  one  which  offers  little  resistance 
to  the  Magnetic  Force;  that  is,  it  is  a  good  conductor  of 

8 


MAGNETISM   AND   PERMANENT  MAGNETS          9 

magnetism  as  compared  with  air.  The  conducting 
power  of  the  all -pervading  Ether  is  taken  as  unity,  and 
is  approximately  the  same  as  that  of  air. 

6.    MAGNETIC  FIELD 

Theory  indicates,  and  experiment  confirms,  that 
magnetism  flows  along  certain  lines  called  Lines  of 
Force,  and  that  these  always  form  closed  paths  or  cir- 
cuits. The  region  about  the  magnet  through  which 
these  lines  pass,  is  called  the  Field  of  Force,  and  the 
path  through  which  they  flow  is  called  the  Magnetic 
Circuit. 

A  magnet  in  the  form  of  a  closed  ring  (Fig.  4)  will 
not  attract  other  magnetic   substances  to  it,  since  an 
excellent  closed  circuit  or  path  is 
provided  in  the  ring  through  which 
the  lines  of  force  pass.     However, 
if  this  ring  be  separated,  as  in  Fig. 
5,  the  magnetic  effect  will  be  pro- 
nounced at  the  points  of  separa- 
tion.    The  opposite  halves  of  the 
ring    will    be    strongly   attracted, 
and  magnetic  substances,  such  as 
iron   or   steel,  will  be  drawn   to,       Closed  Ring  Magnet, 
and  firmly  held  at,  the  points  of  separation. 

The  reason  for  this  is  that  when  the  magnetic  ring  is 
divided,  a  good  path  for  the  lines  of  force  is  no  longer 
provided  at  these  points ;  but,  as  the  air  possesses  unit- 
conducting  power,  the  lines  pass  through  it  and  into 
the  magnetic  ring  again. 

When  a  magnetic  substance  is  brought  near  the 
points  of  separation,  however,  this  magnetic  substance 
offers  a  better  path  for  the  lines  t>f  force  than  the  air  ; 


10  SOLENOIDS 

hence,  as  the  magnetic  field  always  tends  to  shorten 
itself,  thus  producing  a  stress,  the  magnetic  substance 
will  be  drawn  to  the  point  of  sepa- 
ration in  the  magnetized  ring,  and 
into  such  a  position  as  to  form  the 
best  conducting  bridge  across  the 
Air-gap. 

Quite  a  different  effect  is  pro- 
duced when  the  magnet  is  in  the 
form  of  a  straight  bar.  In  this 
case  only  a  part  of  the  magnetic 

circuit  consists  of  a  magnetic  sub- 
Separated  Ring  Magnet.  ,  JIT"         <•   c 

stance ;   hence,  the  lines  of  force 

will  pass  out  through  the  surrounding  air  before  they 
can  again  enter  the  magnet. 

The  paths  of  the  lines  of  force  can  be  demonstrated 
by  placing  a  piece  of  paper  over  a  bar  magnet  and  then 
sprinkling  iron  filings  over  the  paper,  which  should  be 
jarred  slightly  in  order  that  the  filings  may  be  drawn 
into  the  magnetic  paths.  This  effect  is  shown  in 
Fig.  6.* 

7.   PERMANENT  MAGNETS 

Artificial  magnets  which  retain  their  magnetism  for 
a  long  time  are  called  Permanent  Magnets.  These 
are  made  by  magnetizing  hardened  steel,  the  harden- 
ing process  tending  to  cause  the  molecules  of  the  steel 
to  permanently  remain  in  one  direction  when  mag- 
netized. It  is  assumed  that  in  soft  iron  or  steel  the 
molecules  normally  lie  in  such  positions  as  to  neutralize 
any  magnetic  tendency  on  the  part  of  the  material  as  a 
whole. 

*  Made  for  this  vdlume  by  Mr.  E.  T.  Schoonmaker. 


FIG.  6.  —  Field  of  Force  surrounding  Magnet. 


12  SOLENOIDS 

When  the  soft  iron  or  steel  is  placed  in  a  sufficiently 
strong  magnetic  field,  the  molecules  readily  lie  end  to 
end,  so  to  speak ;  thus  possessing  all  the  properties 
necessary  for  a  magnet.  However,  the  molecules 
assume  (approximately)  their  normal  positions  as  soon 
as  the  magnetizing  influence  is  removed  ;  hence,  the 
steel  must  be  hardened  to  produce  a  good  permanent 
magnet. 

Permanent  magnets  are  used  in  electrical  testing 
instruments  where  a  constant  magnetic  field  is  re- 
quired, and  also  as  the  Field  Magnets  or  magnetos,  such 
as  are  extensively  used  on  automobiles  and  in  telephone 
apparatus.  As  these  magnets  have  a  tendency  to  de- 
teriorate with  age,  they  are  artificially  aged  by  placing 
them  in  boiling  water  for  several  hours. 

That  property  which  tends  to  retain  magnetization 
is  known  as  Retentiveness,  and  that  portion  of  magneti- 
zation which  remains  is  called  Residual  Magnetism. 
The  magnetizing  force  necessary  to  remove  all  residual 
magnetism  is  called  the  Coercive  Force.  Soft  iron  has 
little  coercive  force,  but  great  retentiveness ;  while 
hardened  steel  has  great  coercive  force,  but  little 
retentiveness. 

8.    MAGNETIC  POLES 

Although  the  term  North  Pole  is  given  to  that  end 
of  a  bar  magnet  which  points  north,  we  will,  in  this 
book,  make  use  of  the  term  North-seeking  Pole  instead 
of  the  former  term  in  order  to  avoid  confusion  between 
the  north  pole  of  a  magnet  and  the  pole  situated  near 
the  North  Pole  of  the  earth. 

The  strengths  of  the  north-seeking  and  south-seeking 
poles  of  a  magnet  are  equal;  the  strength  diminishing 


MAGNETISM   AND   PERMANENT   MAGNETS        13 

gradually  from  the*  ends  to  the  center  or  Neutral  Point 
of  the  magnet,  where  there  is  no  attraction  whatever. 

Unlike  poles  attract,  while  like  poles  repel  one  another. 

Magnetism  flows  from  the  north-seeking  pole  of  a 
magnet,  through  the  surrounding  region  to  its  south- 
seeking  pole,  and  thence  through  the  inside  of  the 
magnet  to  the  north-seeking  pole.  Reference  to  Fig.  6 
shows  that  all  of  the  magnetic  lines  do  not  flow  from 
the  ends  of  the  magnet,  but  from  all  points  on  the 
north-seeking  portion  to  corresponding  points  on  the 
south-seeking  portion. 

The  theoretical  pole  of  a  magnet  is  regarded  as  a 
point  and  not  as  a  surface ;  hence,  in  practice  the  term 
Pole  is  better  applied  to  the  surface  where  the  density 
of  the  lines  entering  or  leaving  the  magnet  is  greatest. 
The  direction  in  which  the  lines  of  force  flow  indi- 
cates the  Polarity  of  the  magnet  as  previously  described. 
This  explains  why  every  magnet  has  two  poles.  It  is 
evident,  then,  that  no  matter  into  how  many  pieces  a 
permanent  magnet  may  be  separated,  each  piece  will 
be  a  magnet,  since  the  coercive  force  remains  in  each 
piece  and  the  lines  leave  at  one  part  and.  enter  at  an- 
other. Both  poles  will,  therefore,  be  of  equal  strength. 

4  TT  lines  of  force  radiate  from  a  unit  magnetic  pole ; 
for,  if  this  pole  be  placed  at  the  center  of  a  sphere  of 
one  centimeter  radius,  one  line  of  force  per  square  cen- 
timeter will  radiate  from  this  pole,  and  the  area  of  the 
sphere  is  4  vrr2  square  centimeters. 

9.   FORMS  OF  PERMANENT  MAGNETS 
What  may  be  called  the  natural  form  of  permanent 
magnet  is  shown  in  Fig.  7.     This  is  known  as  the  Bar 
Permanent  Magnet,  and  is  the  form  which  constitutes 


14 


SOLENOIDS 


(^  $1    the    compass    needle.     It    is 

not,     however,     an     efficient 

FIG.  7.  —  Bar  Permanent  Magnet. 

form     for     most     purposes, 

owing  to  the  fact  that  its  effective  polar  regions  are 
widely  separated. 

The  practical  permanent 
magnet  consists  of  a  bar  magnet 
bent  into  the  form  of  U,  so  as 
to  shorten  the  magnetic  circuit 
by  bringing  the  polar  regions 
of  the  magnet  close  together. 
This  is  called  a  Horseshoe  per- 
manent magnet,  and  is  shown 
in  Fig.  8. 

A   permanent    magnet   does      I  -J 

work  when  it  attracts  a  piece 

of  iron  or  other  magnetic  sub-  H°^shoe  Permanent  Magnet. 
stance,  called  its  Armature,  to  it.  When  the  armature 
is  forcibly  removed  from  the  magnet,  however,  energy 
is  returned  to  the  magnet.  Since  the  effective  strength 
of  a  magnet  varies  inversely  as  the  resistance  to  the 
magnetic  force,  the  air-gaps  should  be  as  small  as 

possible.  This  is  equiva- 
lent to  stating  that  there 
is  greater  attraction  be- 
tween a  magnet  and  its 
armature  through  a  short 
than  through  a  greater 
distance. 

Another  type  of  horse- 

-i  ,    -        -, 

shoe  magnet  is  shown  in 
Fig.  9.  This  is  said  to  have  Consequent  Poles,  since 
the  ends  of  similar  polarity  are  placed  together.  The 


N\N 


Magnet  with  Consequent  Poles. 


MAGNETISM  AMD   PERMANENT   MAGNETS        15 

same  effect  may  be  obtained 

with  the  arrangement  in  Fig. 

10.    It  is  important,  however, 

that  the  individual  magnets 

constituting    the    Compound 

Magnet  should  have  the  same 

strength   in   order   that   one  Compound  Magnet. 

magnet  may  not  act  as  a  return  circuit  for  the  other, 

thus  weakening  the  combination. 

10.    MAGNETIC  INDUCTION 

When  a  piece  of  iron  is  attracted  by  a  magnet,  it  also 
temporarily  becomes  a  magnet,  and  a  series  of  pieces  of 
iron  will  attract  one  another  successively  so  long  as 
the  first  piece  is  influenced  by  the  magnet.  This  phe- 
nomenon is  said  to  be  the  result  of  Magnetic  Induction. 
In  this  case  the  pieces  of  iron  tend  to  form  a  good  con- 
ducting path  for  the  lines  of  force  ;  hence,  the  more 
perfectly  they  tend  to  close  the  magnetic  circuit,  the 
greater  will  be  their  attraction  for  one  another. 

11.    MAGNETIC  UNITS 

Unit  Strength  of  Pole  is  that  which  repels  another  simi- 
lar and  equal  pole  with  unit  force  (one  dyne)  when  placed 
at  a  unit  distance  (one  centimeter)  from  it.  (Symbol  m.) 

Magnetic  Moment  (symbol  c9/£>)  is  the  product  of  the 
strength  of  either  pole  into  the  distance  between  the  poles. 

Intensity  of  Magnetization  (symbol  C£T)  is  the  mag- 
netic moment  of  a  magnet  divided  by  its  volume. 

&fc  =lm,     (1)  ^=^,  (2) 

wherein  I  =  distance  between  poles 
and          v  =  volume  of  magnet. 


16  SOLENOIDS 

Intensity  of  Magnetic  Field  (symbol  $£>)  is  measured 
by  the  force  it  exerts  upon  a  unit  magnetic  pole,  and, 
therefore,  the  unit  is  the  intensity  of  field  which  acts 
upon  a  unit  pole  with  unit  force  (one  dyne).  The 
unit  is  the  Grauss.  Hence,  one  gauss  is  one  line  of 
force  per  square  centimeter. 


Magnetic  Flux  (symbol  <£)  is  equal  to  the  average 
field  intensity  multiplied  by  the  area.  Its  unit  (one 
line  of  force)  is  the  Maxwell. 

One  gauss  is,  therefore,  equal  to  one  maxwell  per 
square  centimeter. 

Reluctance  or  Magnetic  Resistance  (symbol  cf&)  is  the 
resistance  offered  to  the  magnetic  flux  by  the  material 
magnetized.  The  unit  is  the  Oersted,  and  is  the  reluc- 
tance offered  by  a  cubic  centimeter  of  vacuum. 

Magnetic  Induction  or  Flux  Density  (symbol  68)  is 
the  number  of  magnetic  lines  per  unit  area  of  cross- 
section  of  magnetized  material,  the  area  being  at  every 
point  perpendicular  to  the  direction  of  flux.  The  unit 
is  the  gauss. 

Magnetic  Permeability  (symbol  JJL)  is  the  ratio  of  the 
magnetic  induction  <EB  to  the  field  intensity  £%*  and  is 
the  reciprocal  of  Reluctivity  (specific  magnetic  reluc- 
tance). 


CHAPTER   III 
ELECTRIC  CIRCUIT 

12.    UNITS 

Resistance  (symbol  R)  is  that  property  of  a  material 
that  opposes  the  flow  of  a  current  of  electricity  through 
it.  The  practical  unit  is  the  Ohm,  and  its  value  in 
C.  G.  S.  units  is  109. 

Electromotive  Force  (e.  m.  f.,  symbol  E)  is  the  electric 
pressure  which  forces  the  current  through  a  resistance. 
The  unit  is  the  Volt,  and  its  value  in  C.  G.  S.  units  is  108. 

Difference  of  Potential  is  simply  a  difference  of  elec- 
tric pressure  between  two  points.  The  unit  is  the  Volt. 

Current  (symbol  J)  is  the  intensity  of  the  electric 
current  that  flows  through  a  circuit.  The  unit  is  the 
Ampere.  Its  value  in  C.  G.  S.  units  is  1C"1. 

Ohms  Law.  The  strength  of  the  current  is  equal  to  the 
electromotive  force  divided  hy  the  resistance,  or 

7=  -     (4),  whence  R  =  ^     (5),  and  E  =  IE.   (6) 
R  I 

Conductance  (symbol  6r)  is  the  reciprocal  of  resis- 
tance. The  practical  unit  is  the  M  ho. 

Since  G-  =  -i     (7),  1=  EG     (8),  G-  =  -^     (9),  and 
-,  R  E 


=         (10). 

Cr 


17 


18  SOLENOIDS 

Electric  Energy  (symbol  W)  is  represented  by  the 
work  done  in  a  circuit  or  conductor  by  a  current  flow- 
ing through  it.  The  unit  is  the  Joule,  its  absolute 
value  is  107  ergs,  and  it  represents  the  work  done  by 
the  flow,  for  one  second,  of  1  ampere  through  1  ohm. 

Electric  Power  (symbol  P)  is  1  joule  per  second. 
The  unit  is  the  Watt  and  equals  107  absolute  units. 
745.6  watts  equal  1  horse-power.  1  Kilowatt  equals 
1000  watts. 

Hence,  W=  PT,  (11) 

wherein  W=  energy  in  joules, 

p  —  power  in  watts, 
and  T—  time  in  seconds. 

Now  P  =  EI  (12).  Substituting  the  value  of  P 
from  (12)  in  (11),  W=  EIT.  (13) 

["  6.119  kilogrammeters  per  minute, 
1  watt  =  \  44.26  foot-pounds  per  minute, 
0.001  kilowatt, 
0.00134  horse-power. 

Also  p  =  PR  (14),  =  — .  (15) 

R 

Density  of  Current  in  a  conductor  is  equal  to  the 
total  current  in  amperes  divided  by  the  cross-sectional 

area  of  the  conductor,  or  Id  =  — .  (16) 

-A.w 

When  a  current  of  electricity  flows  through  a  con- 
ductor, heat  is  generated,  due  to  electrical  friction  in 
the  conductor,  and  is  directly  proportional  to  the  watts 
lost  in  the  conductor.  The  resistance  of  a  conductor 
changes  with  its  temperature.  In  nearly  all  cases  the 
resistance  rises  with  the  temperature.  The  ratio 
between  rise  in  temperature  and  rise  in  Resistivity 


ELECTRIC   CIRCUIT  19 

(specific  resistance)  is  called  the  Temperature  Coeffi- 
cient, which  for  copper  is  approximately  0.00388  at 
20°  C.  or  68°  F. ;  that  is,  the  resistance  will  change 
approximately  0.388  per  cent  for  each  degree  Centi- 
grade change  in  temperature.  The  chart  on  p.  300 
gives  the  coefficients  for  different  temperatures. 

Referring  to  equation  (6),  it  is  evident  that  the  vol- 
tage or  e.  m.  f .  per  unit  length  of  conductor  is  propor- 
tional to  the  resistance  per  unit  length,  and  the  strength 
of  the  current  flowing  through  the  conductor. 

The  resistance  is  equal  to  the  length  of  the  con- 
ductor divided  by  its  cross-sectional  area  and  Conduc- 
tivity (specific  conductance),  or 

(IT) 


wherein  lw  —  length  of  conductor, 

Aw  =  cross-sectional  area  of  conductor, 
and  7  =  conductivity  of  material. 

Substituting  the  value  of  R  from  (17)  in  (4), 

E 


and  (6)  then  becomes  E=I*~.  (19) 


Where  the  temperature  is  subject  to  considerable 
change  due  to  either  internal  or  external  influences,  the 
value  of  7  will  vary  ;  hence,  equation  (17)  must  be  used. 

It  is  also  evident  that  where  two  or  more  conductors 
of  different  conductivities,  and  particularly  if  of  the 
same  cross  section,  form  part  of  the  same  electric  cir- 


20 


SOLENOIDS 


cuit,  the  greater  part  of  the  e.  m.  f.  will  be  expended 
in  overcoming  the  resistance  of  the  conductor  having 
the  lowest  value  for  7.  It  will  also  be  evident  that  for 
constant  e.  m.  f.,  the  conductor  having  the  greater  con- 
ductivity will  have  the  greater  density  of  current  when 
singly  connected. 

When  a  conductor  containing  resistance  is  connected 
with  a  source  of  electrical  energy,  such  as  a  battery, 
which  also  offers  some  resistance,  the  conductor  will 
receive  the  maximum  amount  of  electrical  energy  when 
its  resistance  equals  the  sum  of  all  the  other  resistances 
in  the  circuit.  The  rule  is  somewhat  modified  under 
certain  conditions,  as  will  be  seen  by  referring  to  p.  287. 


13.    CIRCUITS 

When  two  or  more  conductors  are  connected  as  in 
Fig.  11,  they  are  said  to  be  in  Series,  and  in  Multiple 

when  connected  as  in 
Fig.  12.     The  latter 
is     called     a    Shunt 
I  circuit. 

FIG.  11.  — Resistances  in  Series.  Consider  two  COn- 

ductors,  each  having  a  resistance  of  100  ohms.  When 
connected  in  series,  the  total  resistance  would  be 
2  x  100  =  200  ohms.  If  connected 
in  multiple,  the  Joint  Resistance 
would  be  l%&  =  50  ohms. 

Hence,  the  series  resistance  is 
four  times  as  great  as  the  multiple 
resistance. 

When  any  number  of  resistances  FIG.  12. 

are   connected   in   series,  the  total    Resistances  in  Multiple. 


ELECTRIC   CIRCUIT 


21 


resistance  will  be  the  sum  of  the  individual  resistances. 
When  any  number  of  equal  resistances  are  connected  in 
multiple,  their  joint  resistance  will  be  the  common 
resistance  of  all  the  circuits  divided  by  the  number  of 
circuits. 

When  two  equal  or  unequal  resistances  are  connected 
in  multiple,  their  joint  resistance  is  equal  to  their  product 
divided  by  their  sum,  or 

RR, 


When  any  number  of  equal  or  unequal  resistances 
are  connected  in  multiple,  the  joint  resistance  is  equal  to 
the  reciprocal  of  their  joint  conductance.  Consider 
three  resistances  Rv  R^  and  Ry  The  conductances  are 

11  1 

-=-*  ^=— ,  and   —  • 


Their  Joint  Conductance  is 


=  Tr  +  -jr  +  TT  = 

i\l       -K^       _n/3 


Hence, 


a,. 


(23) 

In  Fig.  13  is  shown  a  cir- 
cuit consisting  of  a  source 
of  electrical  energy  with  an 
internal  resistance  of  2  ohms, 
an  external  resistance  of 
2.723  ohms,  and  a  shunt 


-AAAAAAA/^ 


.2.723   OHMS 

FIG.  13.  — Divided  Circuit  in 
Series  with  Resistance. 


22  SOLENOIDS 

circuit  consisting  of  three  resistances  of  3,  4,  and  5 
ohms  respectively. 

The  combination  is  connected  in  series,  forming  a 
circuit  partly  in  series  and  partly  m  multiple.  The 
e.  m.  f  .  of  the  battery  is  6  volts. 

The  joint  resistance  of  the  shunt  circuit  is,  from  (23), 

3x4x5  60     .,  Q77    , 

=  —  =  1.277  ohms. 


A 

4x5  +  3x4+3x5     47 

The  total  resistance  in  series  is,  therefore, 

2  +  2.723  +1.277  =  6  ohms. 
Since  J£=  6,  1=  |  =  1  ampere. 

Since  JE=  IR,  the  difference  of  potential  (drop  in 
volts)  across  each  resistance  will  be  as  follows  : 

Drop  in  battery  =1x2         =2  volts 

Drop  in  series  resistance     =  1  x  2.723  =  2.723  volts 
Drop  in  shunt  circuit  =  1  x  1.277  =  1.277  volts 

Total  drop  =6.000  volts 

It  is  thus  seen  that  the  resistances  in  the  series  circuit 
can  be  considered  as  counter  e.  ra./.'s,  and  added  to- 
gether. 

In  shunt  circuits  all  conductances  may  be  considered 
as  currents  and  added  together.  Hence,  in  the  above 
case,  the  conductances  are 

J  =  0.333,  I  =  0.25,  and  -J  =  0.20. 

The  total  current  flowing  through  all  the  branches  at  a 
pressure  of  1  volt  would^  therefore,  be 

1=  0.333  +  0.25  +  0.20  =  0.783  ampere. 


ELECTRIC  CIRCUIT  23 

However,  in  the  case  considered,  the  e.  m.  f.  is  1.277 
volts.  Hence,  the  total  current  will  be  0.783  x  1.277 
=  1  ampere,  and  the  actual  current  flowing  through  each 
branch  will  be 

1.277  x  0.333  =  0.425  ampere, 
1.277  x  0.250  =  0.318  ampere, 
1.277  x  0.200  =  0.257  ampere, 
or  a  total  of  1  ampere. 


CHAPTER   IV 
ELECTROMAGNETIC   CALCULATIONS 

14.   ELECTROMAGNETISM 

WHEN  a  compass  needle  is  placed  near  a  conductor 
through  which  an  electric  current  is  flowing,  the  needle 
tends  to  assume  a  position  at  right  angles  to  the  current 
in  the  wire.  If  the  needle  is  above  the  wire,  and  the 
current  flows  from  left  to  right,  the  north-seeking  pole 
is  deflected  toward  the  observer.  If  the  needle  is  below 
the  wire,  the  north-seeking  pole  is  deflected  from  the 
observer. 

15.    FORCE  SURROUNDING  CURRENT  IN  A  WIRE 

When  an  electric  current  flows,  it  establishes  a  mag- 
netic field  at  right  angles  to  it  in  the  form  of  concentric 


FIG.  14,— Relation  between  Directions  of  Current  and  Force  surrounding  It. 

24 


ELECTROMAGNETIC   CALCULATIONS  25 

circles  of  force.  The  compass  needle,  being  a  magnet, 
is  drawn  by  mutual  attraction  into  such  a  position  that 
its  magnetic  circuit  will  lie  in  the  same  direction  as  the 
lines  of  force  about  the  current.  The  earth's  magnet- 
ism, unless  neutralized,  tends  to  prevent  the  needle 
from  lying  exactly  in  the  direction  of  the  lines  of  force 
due  to  the  current. 

The  relation  between  the  directions  of  current  and 
flux  are  shown  in  Fig.  14. 

16.    ATTRACTION  AND  REPULSION 

Two  wires  lying  parallel  to  one  another,  and  carrying 
currents  in  the  same  direction,  will  be  mutually  at- 
tracted; while  if  the  currents  are  opposite  in  direction, 
they  will  be  mutually  repelled. 

If  a  conductor  carrying  a  current  be  placed  between 
the  poles  of  a  horseshoe  magnet,  and  at  right  angles  to 
the  lines  of  force,  it  will  be  either  attracted  or  repelled, 
according  to  the  relative  directions  of  the  field  due  to 
the  magnet  and  that  due  to  the  current  in  the  wire. 

By  placing  a  loop  of  wire,  through  which  a  current 
is  flowing,  around  a  bar  permanent  magnet  the  same 
general  action  will  result.  If  the  polarities  of  the  loop 
and  magnet  are  the  same,  the  loop  will  tend  to  remain 
at  the  center  of  the  magnet ;  whereas,  if  the  polarities 
are  opposite,  the  loop  will  be  repelled  from  the  magnet 
and  will  not  remain  in  any  position  around  it. 

The  relation  between  the  strength  of  current  in  a  wire 
and  the  intensity  of  magnetic  field  or  Magnetizing  Force 
is  expressed  by  the  equation 

Se=^J,  (24) 


26 


SOLENOIDS 


wherein 

BS=  magnetizing  force  in  gausses, 

I—  current  in  amperes, 

and          a  =  radial  distance  from  center  of  wire  in  centi- 
meters. 

17.    FORCE  DUE  TO  CURRENT  IN  A  CIRCLE  OF  WIRE 
Under  these  conditions  the  lines  of  force  are  distorted, 


as  in  Fig.  15,  but  in  the  center 


0.27T/ 


(25) 


wherein  r  is  the  average 
radius  of  the  turn  of  wire, 
as  in  Fig.  16. 

At  any  distance  x  on  the 
axis  X  the  force  is 

m=Mj&.     (26) 

This  will  be  better  under- 
stood   if    we    consider    the, 
FIG.  15.  — Distortion  of  Field  due     force  at  the  center  by  this 
to  Circular  Current.  formula.       At    the    center 

S=  r.     Therefore,  substituting  r  for  S,  and  referring 
to  equation  (26), 

0. 27rJ 


Since 


(25) 
(28) 
(29) 


From  (25)  is  deduced  the  following  law:  If  a  wire 
one  centimeter  in  length  be  lent  into  an  arc  of  one  centi- 


ELECTROMAGNETIC   CALCULATIONS 


FIG.  16.  —  Strength  of  Field  at  Varying  Distances  from  Center  of  Loop. 

meter  radius,  and  a  current  of  10  amperes  passed  through 
the  wire,  at  the  center  of  the  arc  there  will  be  one  line  of 
force  per  square  centimeter,  i.e.  the  intensity  will  be  one 
gauss. 

18.    AMPERE-TURNS 

One  ampere  flowing  through  one  turn  of  wire  is 
called  one  Ampere-turn.  In  any  case  the  product  of  / 
amperes  into  N  turns  of  wire  equals  ampere-turns. 
Hence,  the  symbol  is  IN.  Since  the  absolute  unit  of 
current  is  equivalent  to  10  amperes,  this  current  flow- 
ing through  one  turn  of  wire  equals  10  ampere-turns, 
and  this  produces  4  TT  dynes,  which  is  the  total  force 
due  to  the  magnetic  pole  of  unit  strength. 

19.    THE  ELECTROMAGNET 

Electric  and  magnetic  circuits  differ  in  the  respect 
that  there  is  no  known  insulator  of  magnetism,  while 
electricity  can  be  insulated.  Thus,  while  dry  air  may 
effectually  insulate  electricity,  it  serves  as  a  unit-con- 
ducting medium  for  magnetism. 


28  SOLENOIDS 

Magnetism  cannot  be  efficiently  transmitted  over  any 
great  distance  on  account  of  leakage.  The  practical 
method  is  to  transmit  a  current  of  electricity  through  a 
wire,  and  then  convert  its  energy  into  magnetism  at 
the  point  where  the  attraction  is  desired. 

This  is  accomplished  by  winding  spirals  of  insulated 
wire  around  the  magnetic  material  which  is  to  be  mag- 
netized. Such  a  device  is  known  as  an  Electromagnet, 
and  upon  the  passage  of  an  electric  current  through  the 
winding,  the  magnetic  material  behaves  similarly  to  a 
permanent  magnet  of  the  same  general  form,  with  the 
exception  that,  if  the  magnetic  material  has  but  little 
coercive  force,  the  magnetism  will  practically  disappear 
upon  the  discontinuation  of  the  electric  current  through 
the  winding. 

20.    EFFECT  OF  PERMEABILITY 

The  permeability  or  magnetic  conductivity  of  mag- 
netic materials,  such  as  iron  or  steel,  decreases  as  the 
flux  density  increases.  The  relation  is  expressed 

fi  =  ^  (30) 

86 

wherein    p  =  permeability, 

68=  magnetic  induction  or  flux  density, 
and         B8  =  magnetizing  force  or  intensity  of  field. 

Figure  17  shows  the  variation  in  permeability  for  dif- 
ferent values  of  69.  This  is  called  the  Permeability 
Curve.  Such  curves  are  obtained  from  iron  and  steel  by 
actual  tests,  and  these  data  used  in  subsequent  calcu- 
lations. The  table  on  p.  323  will  be  found  useful. 


ELECTROMAGNETIC   CALCULATIONS 


29 


3,600 
3,200 
2,800 
2,400 
2,  ooo 
/,600 

goo 

^00 

o 

. 

— 

/ 

\ 

\ 

I 

\ 

1 

\ 

1 

\ 

J\ 

\ 

\ 

\~. 

•  

§OOOQ          oOOOQ 
oOooooo°Q 

£       0         0        §        Ci          00         0        0       Q 

FIG.  17.  — Permeability  Curve. 


21.   SATURATION 

In  Fig.  18  is  shown  the  general  relations  between  &6 
and  6B.  This  is  known  as  the  Magnetization  Curve. 
Similar  curves  are  shown  in  Fig.  20,  which  will  be 
referred  to  later.  The  point,  where  the  flux  density  or 
induction  6B  is  not  materially  increased  by  a  consider- 
able increase  in  the  magnetizing  force  BS  is  called  the 
Saturation  Point,  or  Limit  of  Magnetization,  and  at  this 
point  the  iron  or  steel  is  said  to  be  Saturated. 


30 


SOLENOIDS 


..^—  '  

-           - 

—   i       — 

• 

X 

/ 

LJ 

°         ioo<oQ<oO(0o«r»o 

Fia.  18.  —  Magnetization  Curve. 

The  values  *  of  €&  at  the  saturation  point,  for  various 
grades  of  iron  and  steel,  are  as  follows: 

Wrought  iron 20,200 

Cast  steel 19,800 

Mitis  iron 19,000 

Ordinary  cast  iron    .....  12,000 

The  practical  working  densities  are  about  two  thirds 
of  the  above  values  and  are  as  follows: 


Wrought  iron  . 
Cast  steel 


13,500 
13,200 


*  Wiener,  Dynamo-electric  Machines. 


ELECTROMAGNETIC   CALCULATIONS 


31 


Mitis  iron  .  12,700 

Ordinary  cast  iron    .         .  8,000 

The  permeability  should  not  fall  below  200  to  300. 


22.    SATURATION  EXPRESSED  IN  PER  CENT 

The  amount  of  saturation  of  a  given  flux  path  may 
be  conveniently  expressed  in  per  cent.     It  is  obvious 


Flux 

12 1— 


Magnetizing  Force 


2  a 
1 


a"  10 
5 


FIG.  19.  —  Saturation  Curve  plotted  to  Different  Horizontal  Scales. 

that  the  statement  that  a  magnet "  is  worked  well  up  to 
the  knee"  or  "well  below  the  knee"  means  very  little 
when  any  degree  of  accuracy  is  desired.  This  arbi- 
trary method  of  denning  saturation  is  deceptive  because 
the  position  of  "  the  knee  "  depends  upon  the  scales  to 
which  the  saturation  curve  is  plotted,  as  will  be  seen 
by  reference  to  Fig.  19,  all  the  curves  being  plotted 
from  the  same  data  except  that  they  are  drawn  to 
different  scales. 


32  SOLENOIDS 

What  is  desired  is  a  definition  which  will  indicate 
100  per  cent  saturation  for  the  condition  in  which 
there  is  no  increase  of  flux  for  an  increase  of  magnetiz- 
ing force,  and  will  indicate  zero  saturation  for  the  condi- 
tion in  which  the  flux  increases  proportionally  to  the 
magnetizing  force. 

Mr.  H.  S.  Baker  has  proposed  the  following  method  :  * 
Draw  a  tangent  to  the  saturation  curve  (at  point  under 
consideration),  cutting  the  Y  axis.  The  percentage  of 
saturation  is  the  percentage  that  the  intercept  (OT)  on 
the  Y  axis  is  of  the  ordinate  (ab)  of  the  point.  It  will 
be  seen  that  this  definition  is  independent  of  the  scales 
to  which  the  curve  is  plotted,  as  indicated  by  similar 
points  (£,  6',  and  b")  on  the  saturation  curves  shown 
plotted  to  different  scales.  Thus  the  percentage  of 
saturation  of  the  point  b  is 

100  x  —  =75.2. 

ab 

23.   LAW  OF  MAGNETIC  CIRCUIT 

Magnetomotive  Force  (m.  m.  f.,  symbol  c/0  is  the  total 
magnetizing  force  developed  in  a  magnetic  circuit  by  a 
coil  of  wire  through  which  a  current  is  flowing.  The 
unit  is  the  Gilbert,  gr  =  0.4  ,r  ZZV.  (31) 

The  magnetizing  force  is  equal  to  the  gilberts  per 
centimeter  length, 


or  98  =  f,    (32)     =  ,  (33) 

^m  ^m 

wherein  lm  —  mean  length  of  magnetic  circuit  in  centi- 
meters. 

*  Electrical  World  and  Engineer,  Vol.  XLVI,  1905,  p.  1037. 


ELECTROMAGNETIC   CALCULATIONS  33 

What  may  be  called  the  Ohm's  law  of  the  magnetic 
circuit  is  as  follows:  The  flux  is  equal  to  the  magnetomo- 
tive force  divided  by  the  reluctance, 

*-£  (34) 

By  rearrangement, 

(35)  <^  =  f-  (36) 


In  air  the  reluctance  is  constant,  and  is  proportional 
to  the  length  of  the  air-gap  divided  by  its  cross-sec- 
tioiial  area,  but  in  any  magnetic  material 

<^  =  -K  (37) 

AII, 

wherein      lm  =  mean  length  of  magnetic  circuit, 

A  =  cross-sectional  area, 
and  yit  =  permeability. 

Substituting  values  of  £f  and  cfc  from  (31)  and  (37) 

(38) 


Since  86  =  ^,  (32) 

^m 

(39)  becomes  <f>  =  BSA^i.  (40) 


Now  <S8  =  4-  (41) 

A 


34  SOLENOIDS 

Substituting  the  value  of  6B  in  (40), 


(42) 

whence  86=—.  (43) 

H 

Substituting  the  value  of  &8  from  (33)  in  (42), 

(     IN=  °-7958  ™*,  (44) 


whence  £B  =    .  (4g) 

^m 

24.    PRACTICAL  CALCULATION  OF  MAGNETIC 
CIRCUIT 

Equation  (45)  shows  that  for  any  specific  case  the 
induction  £&  is  proportional  to  the  ampere-turns  per 
centimeter  length  of  magnetic  circuit.  By  means  of 
the  curves  in  Fig.  20  *  the  proper  ampere-turns  may  be 
quickly  determined,  since  the  total  number  of  ampere- 
turns  required  to  maintain  the  induction  <93  is  equal  to 
the  product  of  the  length  of  the  magnetic  circuit  into 
the  ampere-turns  per  centimeter  length. 

As  an  example,  assume  that  13,500  lines  per  square 
centimeter  or  13.5  kilogausses  are  required  in  a  wrought- 
iron  ring,  the  average  length  of  the  magnetic  circuit 
being  25  cm.  Referring  to  Fig.  20,  there  are  required 
for  13,500  lines  per  square  centimeter  7.5  ampere-turns 
for  each  centimeter  length  of  magnetic  circuit.  Hence, 
the  total  ampere-turns  will  be  25  x  7.5  =  187.5. 

As  a  rule,  the  magnetic  circuit  consists  of  a  uniform 
quality  of  iron.  Hence,  when  the  cross-section  varies, 

*  From  Foster's  Electrical  Engineer's  Pocket  Book,  by  permission 
of  D.  Van  Nostrand  Co. 


ELECTROMAGNETIC   CALCULATIONS 


35 


§        r         •       3       «        B       3 

HONI  aavnos  aad  snaMxvNOiix 

FIG.  20.  —  Ampere-turns  per  Unit  Length  of  Magnetic  Circuit. 


36 


SOLENOIDS 


the  induction  may  be  calculated  for  one  part  of  the 
circuit  and  then,  for  the  other  parts,  the  induction  will 
simply  depend  on  the  ratio  of  their  cross-sections  to 
the  cross-section  of  the  first  part. 

Where  they  occur,  the  ampere-turns  for  the  air-gaps 
may  be  calculated  by  equation  (44).  Allowances  must 
also  be  made  for  the  curvature  of  the  lines  in  air-gaps, 
and  for  joints,  cracks,  etc.  Joints  should  be  carefully 
faced,  and  the  cross-sectional  area  should  at  least  equal 
that  of  the  part  having  the  lowest  permeability. 

The  above  applies  to  closed  magnetic  circuits  with 
small  air-gaps,  no  leakage  being  considered. 


25.   MAGNETIC  LEAKAGE 

Just  as  electric  currents  in  divided  or  branched  circuits 

are  proportional  to  the 
conductances  of  these 
circuits,  so  too  is  the 
number  of  magnetic  lines 
flowing  through  iron 
and  air  in  shunt  with  one 
another  proportional  to 
the  Permeances  of  iron 
and  air.  As  previously 
stated,  the  permeability 
of  air  is  unity  for  all  flux 
densities,  while  that  of 
iron  or  steel  changes 
with  the  flux  density. 

Figures    21     to     23 
show  the  leakage  paths 
very  nicely  for  an  iron  ring.     It  will  be  observed  that  in 


ELECTROMAGNETIC   CALCULATIONS 


37 


Fig.  21,  where  the  wind- 
ing is  evenly  distributed 
over  the  iron  ring,  there 
are  no  leakage  lines ; 
whereas,  in  Fig.  22,  in 
which  but  a  small  por- 
tion of  the  iron  ring  is 
wound  with  insulated 
wire,  there  is  some  leak- 
age which  is  propor- 
tional to  the  relative 
reluctances  of  the  iron 
ring  and  the  air  space. 
The  leakage  around  the 
air-gap  in  Fig.  23  is 
very  marked. 


FIG.  22.  —  Leakage  Paths. 

The  ratio  between  the  total  number  of  lines  generated 

and  the  number  of  use- 
ful lines  is  called  the 
Leakage  Coefficient,  and 
is  denoted  by  the 
symbol  Vt.  Thus, 

r,=%,        (46) 


wherein  <j>t  =  total  flux, 
and     <j)g  =  useful    flux 

through  air-gap. 

The  reluctance  be- 
tween two  flat  sur- 
faces is 

(37) 


FIG.  23.  —  Leakage  Paths  around  Air-gap. 


38  SOLENOIDS 

but  between  two  cylinders  *  it  is 


(47) 


i  a  dc 

wherein 


ai     b  -  y  62  _  d? 
dc  =  diameter  of  the  cylinders, 
b  =  distance  between  centers, 
and  lc  —  length  of  cylinders. 

The  numerical  value  of  —  is  constant  for  all  dimen- 

ai 

sions  as  long  as  the  ratio  —  is  constant. 

ac 

Figure  24  f  shows  the  magnetic  reluctance  per  centi- 
meter between  two  parallel  cylinders  surrounded  by 

air,  and  having  various  values  of  the  ratio  — . 

dc 

The  total  reluctance  between  two  cylinders  is  the 
reluctance  per  centimeter  divided  by  the  length  of  each 
cylinder  in  centimeters.  Since  at  the  yoke  the  m.  m.  f. 
is  approximately  zero,  and  at  the  poles  it  is  approxi- 
mately maximum,  the  average 


m.  m.  f.  =  =  0-2  wiy.  (48) 


Therefore,  the  leakage  is 

0.2 


*  Jackson's  Electromaynetism  and  the  Construction  of  Dynamos. 
f  Plotted  from  table  in  Jackson's  Electromagnetism  and  the  Con- 
struction of  Dynamos. 


ELECTROMAGNETIC   CALCULATIONS 


39 


c^h  being  found   from   the   curve  as  explained  above. 
From  this  the  leakage  coefficient  VL  is  found. 


FIG.  24.  —  Reluctance  between  Cylinders. 

The  leakage  may  be  included  in  the  total  reluctance 
by  multiplying  the  sum  of  the  reluctances  by  the  leak- 
age coefficient. 


Thus' 


=  V, 


(50) 


Only  approximate  results  may  be  obtained  by  this 
method  since  the  m.  m.  f.  between  the  poles  cannot  be 
considered  as  the  total  m.  m.  f. 


CHAPTER   V 
THE   SOLENOID 

26.    DEFINITION 

AN  electrical  conductor  when  wound  in  the  form  of  a 
helix  is  called  a  Solenoid,  and  when  a  current  of  elec- 
tricity is  passed  through  the  turns  of  wire,  it  possesses 
many  of  the  characteristics  of  the  bar  permanent  mag- 
net, so  far  as  its  magnetic  field  is  concerned. 

As  was  explained  in  Art.  17,  when  a  conductor  carry- 
ing a  current  is  bent  into  the  form  of  a  circle,  the  lines 
of  force  pass  through  the  region  inside  of  the  loop.  Now, 


FIG.  25.  —  Sixteen-turn  Coil.  FIG.  26.  —  One-turn  Coil. 

when  several  turns  of  wire  are  wound  in  close  proximity, 
and  a  current  flows  through  them,  the  lines  of  force  due 
to  the  current  in  each  turn  unite,  and  the  magnetic  field 
is  similar  to  what  it  would  be  if  a  solid  ring  of  conduct- 
ing material  were  used  instead  of  the  several  turns  of 
wire. 

Referring  to  Figs.  25  and  26,.  sixteen  turns  of  wire, 
carrying  100  amperes  each,  may  be  considered  as  equiva- 
lent to  one  turn  carrying  1600  amperes  ;  the  ampere- 
turns  and,  consequently,  the  magnetic  effect  will  be 

40 


THE   SOLENOID  41 

practically  the  same  in  both  cases.  Any  coil  or  wind- 
ing, no  matter  how  long,  or  how  coarse  or  fine  the  wire 
used,  may  be  considered  in  the  same  light,  providing  the 
turns  are  not  farther  apart  than  in  ordinary  practice. 

The  internal  magnetic  field  of  a  solenoid  in  which  the 
length  of  the  winding  is  great,  as  compared  to  its  aver- 
age radius,  is  very  uniform,  and  this  fact  is  taken  advan- 
tage of  in  the  type  of  electromagnet  known  as  the  Coil- 
and-Plunger,  but  more  commonly  called  the  solenoid. 

As  was  explained  in  Art.  16,  mutual  attraction  exists 
between  a  coil  of  wire  carrying  a  current  and  a  magne- 
tized rod  of  steel.  This  attraction  is  the  result  of  the  in- 
terlinking of  the  lines  of  force  due  to  the  current  in  the 
coil,  and  those  existing  in  and  about  the  steel  bar.  In 
this  case  attraction  or  repulsion  will  occur,  depending 
upon  the  relative  directions  of  the  magnetic  fields,  the 
bar  being  drawn  inside  the  winding  or  repelled,  as  the 
case  may  be. 

Magnetized  steel  bars  cannot,  however,  be  used,  prac- 
tically, to  obtain  repulsion,  owing  to  the  demagnetizing 
effect  on  the  steel  bar  when  the  polarity  of  the  field  due 
to  the  current  in  the  coil  is  reversed.  Common  types 
of  solenoids  have  soft  iron  or  steel  plungers,  as  the  bars 
of  magnetic  material  are  called. 

The  solenoid,  in  one  of  its  simplest  forms,  consists, 
essentially,  of  the  winding  of  helices  of  right  and  left 
pitch    and    the    supporting    ^ggBgjjSBjjM 
ends,  as  shown  in  Fig.   27. 
Solenoids  with  soft  iron  or    i^i^iniriv-"^^--.^ 
steel  plungers  are  automatic        FlG'  27'~ Siraple  Soleuoid- 
in  their  action,  the  plunger  being  magnetized  by  the 
field  of  the  excited  coil,  and  mutual  attraction  then 
results  between  the  field  of  the  coil  and  the  induced 


42  SOLENOIDS 

field  of  the  plunger,  and  if  the  coil  be  stationary  and 
the  plunger  be  free  to  move,  the  latter  will  be  drawn 
within  the  coil  until  the  center  or  neutral  point  of  the 
plunger  is  at  the  center  of  the  coil,  and  force  will  be 
required  to  change  the  relative  positions  of  the  coil  and 
plunger  in  either  direction. 

27.    FORCE  DUE  TO  SINGLE  TURN 

In  order  to  thoroughly  understand  the  action  of  the 
solenoid  on  its  plunger,  consider  again  the  loop  or  sin- 
gle turn  of  wire  through  which  a  current  is  passing. 
(See  Art.  17,  p.  26.) 

Now  the  magnetizing  force  along  the  center  line  or 
axis  of  the  turn  is 

(29) 


wherein  r  is  the  radius  as  measured  from  the  center  of 
the  wire  to  the  axis  of  the  loop,  and  x  is  any  distance 
from  the  vertical  center  of  the  loop  on  its  axis,  in  either 
direction.  It  will  be  seen  that  B8  is  not  only  depend- 
ent upon  the  strength  of  the  current,  but  also  upon  the 
radius  of  the  loop  and  the  distance  x. 
By  reducing  0.2  Tr/to  unity, 


and  the  characteristics  of  the  loops  and  groups  of  loops 
may  now  be  studied  without  considering  the  actual 
current  flowing  through  the  wire.  2 

In  Fig.  28  are  shown  the  values  for  -  -  with 

(r*+x*y 

values  of  r  from  1  to  14  and  distances  x  from  0  to  10. 
r  and  x  are  expressed  in  centimeters.  While  the  chart 


THE   SOLENOID 


Fia.  28.  — Force  due  to  Turns  of  Different  Radii. 


44  SOLENOIDS 

only  shows  the  curves  on  one  side  of  the  vertical  center 
line  of  the  loop,  the  curves  at  the  left-hand  side  would 
be  exactly  similar,  falling  away  from  the  relatively  high 
values  at  the  center  of  the  loop  to  lower  values  as  the 
distance  x  increases. 


When  r  =  x,      —  -       =  .    The  factor  0.3536 


is  merely  —  .     It  will  also  be  observed  that  when  r  =  x, 

2* 

the  curve  for  twice  the  value  of  r,  that  is,  2r,  intersects 
with  r  and  x  at  nearly  the  same  point.  Thus,  the  r  =  6 
curve  intersects  with  the  r=  3  curve  at  x—  3.  This  is 
due  to  the  fact  that  when  r  =  x, 

=0.3536  Vr, 


and  when  r  =  2  #, 

(2*)2       =  Q.358V;. 


A 

Assigning  0  to  -  —  ,  these  relations  may  be  ex- 


pressed    0  =  and     0  =     °-858  Hence,  'if 


r  =  6,  at  -  •  =  3  cm.  from  the  vertical  center  of  the  loop 


(=*)    the   value   of  0  will  be  =  0.1193;   or  if 


. 

o 

It  is  seen  that  where  the  radius  r  is  small,  the  force 
along  the  horizontal  axis  is  great  for  small  values  of  #, 
whereas  with  the  larger  radii,  the  force  is  more  uniform, 


THE   SOLENOID  45 

and  is  greater  for  large  values  of  x  than  for  the  turns  of 
smaller  radii. 

The  equation  0  =    '  shows  that  a  curve  drawn 

(r=x) 

through  the  various  points  of  intersection  of  r  and  #, 
where  r  =  x,  would  be  a  rectangular  hyperbola,  which 
indicates  that  the  total  work  done  in  moving  a  unit 
magnetic  pole  from  an  infinite  distance  to  the  vertical 
center  line  of  the  turn  of  wire  along  the  horizontal  axis 
would  be  the  same  in  all  cases. 

28.    FORCE  DUE  TO    SEVERAL   TURNS    ONE    CENTI- 
METER APART 

The  practical  solenoid  consists  of  many  layers  of  wire, 
each  layer  consisting  of  a  great  many  turns.  Hence,  it 
is  necessary  to  know  what  relation  exists  between  a 
single  turn  and  a  great  many  turns. 

Consider  two  turns  of  wire  of  2  cm.  radius,  arranged 
side  by  side  and  1  cm.  apart,  center  to  center,  with  the 
same  amount  of  current  flowing  through  each. 

Referring  to  the  chart,  Fig.  28,  it  is  seen  that  at  the 
center  of  each  turn  of  wire  6=  0.5,  and  at  1  cm.  on 
each  side  6  =  0.358.  It  is  obvious,  then,  that  the  total 
force  at  the  center  of  each  turn  will  be  the  sum  of  the 
forces  due  to  each  turn,  and  this  will  be  proportional  to 
0.5  +  0.358  =  0.858. 

Likewise,  if  another  turn  be  added  under  similar  con- 
ditions, the  force  may  be  determined  as  follows: 

TURN  1 

0  at  center    .......  0.500 

6  due  to  turn  2,  1  cm.  distant         .         .         .  0.358 

6  due  to  turn  3,  2  cm.  distant        .         .         .  0.117 

0Ll  =  total  force  for  turn  1     ....  1.035 


46  SOLENOIDS 

TURN  2 

6  at  center .  0.500 

0  due  to  turn  1,  1  cm.  distant        .         .         .  0.358 

0  due  to  turn  3,  1  cm.  distant        .         .         .  0.358 

#z2  =  total  force  for  turn  2   ....'.         .         .  1.216 

TURN  3 

0  at  center 0.500 

0  due  to  turn  2,  1  cm.  distant        .         .         .  0.358 

6  due  to  turn  1,  2  cm.  distant        .         .         .  0.177 

^zs  =  total  force  for  turn  3      ....  1.035 

In  the  above,  6L  indicates  the  force  due  to  several 
turns  arranged   side   by    side,    all   being   of   the  same 

radius    and    6LV    etc.,    indicates    the    number  of    the 
turn. 

Adding  one  more  turn,  the  following  is  obtained: 

TURN  1 

6  at  center    .......  0.500 

6  due  to  turn  2,  1  cm.  distant         .         .         .  0.358 

6  due  to  turn  3,  2  cm.  distant        .         .         .  0.177 

0  due  to  turn  4,  3  cm.  distant        .         .         .  0.085 

0L1  =  total  force  for  turn  1     .          .          .          .  1.120 

TURN  2 

6  at  center 0.500 

0  due  to  turn  1,  1  cm.  distant      •   .          .          .  0.358 

6  due  to  turn  3,  1  cm.  distant          .          .          .  0.358 

0  due  to  turn  4,  2  cm.  distant         .         .          .  0.177 

0    =  total  force  for  turn  2     .  1.393 


THE  SOLENOID  47 

TURN  3 

0  at  center 0.500 

6  due  to  turn  2,  1  cm.  distant        .         .         .  0.358 

6  due  to  turn  4,  1  cm.  distant         ...  0.358 

6  due  to  turn  1,  2  cm.  distant         .          .          .  0.177 

0L3=  total  force  for  turn  3     ....  1.393 

TUKN  4 

6  at  center 0.500 

6  due  to  turn  3,  1  cm.  distant         .         .         .  0.358 

0  due  to  turn  2,  2  cm.  apart  .         .         .         .  0.177 

6  due  to  turn  1,  3  cm.  distant         .          .          .  0.085 

0X4  =  total  force  for  turn  4     ....  1.120 

This  procedure  may  be  continued  indefinitely. 

A  little  reflection  will  show  that  the  sums  of  the 
values  of  6  may  be  expressed  in  the  following  arrange- 
ment, wherein  6l  represents  the  value  of  6  for  the  first 
(central)  turn,  02  the  value  of  0  for  the  second  (adjoin- 
ing) turn,  etc. 

No.  OF 
TURNS 

1.      0,. 

3.  02  +  0l4-02. 

5.  fls+fla  +  ^  +  ^  +  tfs. 

7.  0,  +  03  +  #2  +  #1  +  ei  +  #3  +  04- 

9.  05  +  04  +  08  +  02  +  01  +  0a  +  08+04+06. 

If  Nc  =  the  number  of  turns,  or  groups  of  turns,  of 
wire,  m  =  the  number  of  the  central  turn  or  group,  and 
0Lm  =  tne  sum  of  the  values  of  0  =  total  0  at  the  center 


co 


THE   SOLENOID 


49 


of  the  coil  when  the  turns  or  groups  are  1  cm.  apart, 
center  to  center, 

then  0LM  =  2  (^  +  •  •  -  6m)  -  Or  (51) 

The  sums  of  01  to  010,  for  various  radii,  are  shown  in 
Fig.  29. 

29.  FORCE  DUE  TO  SEVERAL  TURNS  PLACED  OVER 

ONE  ANOTHER 

A  method  of  calculating  the  force  at  the  center  of  a 
coil  of  any  length  and  radius  (this 
will  be  the  average  radius  in  the 
case  of  any  wire  or  group  of  wires 
larger  than  a  point)  with  unit  thick- 
ness or  depth,  T  (in  the  case  of 
groups  of  wires),  has  been  given. 
It  now  remains  to  calculate  the 
total  force  for  solenoids  of  any 
thickness  and  any  radius.  It  is 
obvious  that  if  the  successive  addi- 
tion of  the  forces  due  to  adjoining 
turns  gives  the  total  force,  so  should  — 
the  addition  of  the  forces  due  to 
several  turns  or  groups  placed  one 
over  another  give  the  total  force  at 
the  center  due  to  all  the  turns. 

Consider  the  arrangement  in  Fig. 

30.  Each  square  may  be  assumed 
to  represent  either  a  solid  conduc- 
tor or  a  group  of  smaller  conductors 
insulated  from  one  another,  the  total 
ampere-turns    beinff    the    same    in      F™-  a°-— Groups  of 

Turns  placed   over 
each   Square.  One  Another. 


50  SOLENOIDS 

At  the  center  of  a  loop  of  wire 

8g  =  M.*I,  (25) 

9&  =  °-^™,  (52) 

where  there  is  more  than  one  turn,  and  since,  in  this 
case,*  =  0,  0  =  -  ^—  =     =  1. 


The  sum  of  the  forces  at  the  center  of  the  coil  in 
Fig.  30  will,  therefore,  be 

30_l07_0,1 
~~ 


210 

The  magnetizing  force  at  the  center  may  also  be  cal- 
culated direct  from  the  mean  magnetic  radius  of  the  coil 
in  Fig.  80,  which  is  known  as  a  disk  solenoid  or  disk 
winding. 

The  mean  magnetic  radius  is  equal  to  the  reciprocal  of 
the  sum  of  the  reciprocals  of  the  average  radii  of  the  squares 
or  groups  of  turns  constituting  the  disk,  multiplied  by  the 
number  of  squares. 

Now  the  average  radius  ra  is  6,  but  the  mean  mag- 
netic radius  is 


wherein  Ng  is  the  number  of  groups,  and  rc,  rrf,  and  re, 
etc.,  are  the  respective  average  radii  of  the  groups  of 
turns. 

Hence,  in  the  case  considered, 
8(5x6x7) 


x7)  +  (7  x5)      107 


THE   SOLENOID 


51 


and  since  0V=  -  for  one  group,  for  the  three  groups 


as  in  the  previous  case. 


30.   FORCE  DUE  TO   SEVERAL   DISKS   PLACED    SIDE 
BY  SIDE 


Having  found  the  relations 
consider  the  effect  of  placing 
several  of  the  disks  side  by 
side,  as  in  the  case  of  the 
loops  of  the  same  radii.  For 
this  purpose  the  disk  winding 
in  Fig.  30  will  be  selected, 
since  its  constants  have  al- 
ready been  calculated. 

Arranging  three  such  disks 
side  by  side,  which  will  make 
the  distance  apart,  center  to 
center,  one  centimeter,  they 
will  appear  as  in  Fig.  31. 

Substituting  2*  for  Ng,  which 
expresses  the  vertical  thickness 
of  the  winding,  and  assigning 
L  to  the  length  of  the  winding, 
the  values  will  be  T=3,  L=%. 

Calculating  on  the  same 
principle  as  used  in  the  deter- 
mination of  the  force  at  the 
center  of  a  group  of  single 
loops  placed  side  by  side,  it  is 


for  the  disk  winding, 


3   CMS.-* 


T 


FIG.  31. — Groups  of  Turns  ar- 
ranged to  form  a  Large  Square 
Group. 


52  SOLENOIDS 

obvious  that  the  force  at  any  point  x  on  the  axis  of  a 
single  disk  will  be 

TV    2 

*.=  -     -±a--  (55) 


Hence,  when   x  =  1, 


(1  +  34.67)2 

while  at  the  center  of  each  disk,  0V  =  0.51. 

Following  the  same  general  procedure  as  given  on 
p.  50,  there  results  for  the  total  force  Os  at  the  center 
of  the  entire  square  winding, 

0,  =  0.  +  0Vi  +  0,a  =  0.51  +  0.489  +  0.489  =  1.488. 

In  practice  it  is  customary  to  express  the  magnetiz- 
ing force  in  terms  of  ampere-turns  per  centimeter 

cf 

length,  since  eft?  is  proportional  to  —  ,  wherein  £f  is  the 

I'm 

magnetomotive  force  (m.  m.  f.),  and  lm  is  the  mean 
length  of  the  magnetic  circuit  in  centimeters,  and  re- 
gardless of  the  thickness  of  the  winding,  T.  Hence, 
in  this  case  the  force  at  the  center  is 


=  0.496, 


wherein  6t  is  the  factor  to  be  multiplied  by  0.2  TrIN  to 
give  the  value  of  £f6  at  the  center  of  the  winding. 

The  same  result  may,  of  course,  be  obtained  by  cal- 
culating the  force  due  to  three  coils  of  average  radii 
5  cm.,  6  cm.,  and  7  cm.,  respectively,  each  being  3  cm. 
in  length.  This  gives'the  following  result: 


THE   SOLENOID 


53 


6L  due  to  inner  coil 
0L  due  to  middle  coil 
0L  due  to  outer  coil 


Hence, 


0.578 

0.487 

0.420 

Qs=  total  at  center  =  1.485 


1.485 
3 


=  0.495. 


While  so  exact  values  cannot  be  read  from  a  chart 
as  may  be  obtained  by  direct  calculation,  the  former 
are  near  enough  in  practice.  The  value  of  the  charts 
will  be  appreciated  when  it  is  considered  that  the 
formula  for  a  simple  coil  where  L  =  2  and  T=3 
would  be 


a+o* 


(57) 


or 


rn       r. 


wherein 


(58) 


,  and  ra  are  the  radii  of  the  inner,  middle, 


and  outer  squares  or  groups  respectively. 


54  SOLENOIDS 

31.    FOKCE   AT   CENTER    OF   ANY   WINDING   OF 
SQUARE  CROSS-SECTION 

Since  the  rule  0  =  -  holds  for  a  single  loop  or  group 

of  turns  one  square  centimeter  in  cross-section,  it  is 
obvious  that  a  slight  modification  of  this  rule  should 
apply  to  the  total  force  at  the  center  of  any  winding 
of  square  cross-section. 

This  relation  may  be  expressed  6t  —  —  (59)  (nearly), 

ra 

wherein  L  is  the  length,  and  ra  the  average  radius  of 
the  winding. 

Applying  this  formula  to  the  coil  in  Fig.  31,  there 
results  ^  =  |  =  0.5. 

This  type  of  solenoid  is  sometimes  called  a  rim  sole- 
noid in  contradistinction  to  the  disk  solenoid. 

32.    TESTS  OF  RIM  AND  DISK  SOLENOIDS 

The  following  tests  *  which  were  made  by  the  author 
will  be  of  interest  in  proving  the  foregoing  formulae. 

Two  sets,  each  consisting  of  four  flat  spools  or  bobbins 

of  varying  outside  diam- 
eters, were  prepared  with 
a  hole  in  the  center  of 
each  large  enough  to  re- 
ceive a  plunger  2.87  cm. 
in  diameter.  The  cross- 
sectional  area  of  the 
plunger  was,  therefore, 
6.45  sq.  cm. 

FIG.  32.  —  The  Test  Solenoids.  Figure    32    sllOWS   the 

*  Electrical  World  and  Engineer,  Vol.  XVI,  1905,  pp.  615-617. 


THE   SOLENOID 


55 


general  appearance  of  each  set,  while  the  actual  dimen- 
sions of  the  rim  and  disk  solenoids  are  shown  in  Figs. 
33  and  34. 


FIG.  33.  —  Dimensions  of  Rim  Solenoids. 

The  length  of  the  plunger  was  one  meter.     Of  course, 
a  shorter  plunger  could  have  been  used,  but  it  was  de- 


56 


SOLENOIDS 


sired  to  have  a  plunger  of  sufficient  length  to  make  the 
conditions  of  the  test  as  ideal  as  possible.     The  cross- 


MS>\ 


FIG.  34.  —  Dimensions  of  Disk  Solenoids. 


sectional  area  of  the  plunger  was  purposely  made  the 
same  as  the  cross-sectional  area  of  the  rim  solenoids. 


THE   SOLENOID 


57 


FIG.  35.  — Method  of  testing  Rim  and  Disk 
Solenoids. 


The   tests  were  made  by  the  method   illustrated  in 
Fig.  35.     Here  A  is  a  magnetizing  coil  to  saturate  the 
core,  and  B  repre- 
sents the  winding 
to  be  tested. 

First  the  coil  A 
was  excited  so  as 
to  thoroughly  sat- 
urate the  iron  core, 
and  then  a  disk 
winding  was 
placed  over  the  end  of  the  core  in  the  position  of  maxi- 
mum pull,  and  excited  from  a  separate  source.  Each  coil 
had  a  rheostat  and  ammeter  in  series,  the  two  coils  being 
so  connected  that  attraction  would  result.  Coil  A  was 
rigidly  fastened  to  the  iron  core,  and  the  test  coil  B 
attached  to  the  scales. 

After  the  core  was  saturated,  a  change  in  the  strength 
of  the  current  in  coil  A  produced  an  almost  inappreciable 
change  in  the  pull,  which  was  accredited  to  the  change  in 
eft?;  but  when  the  current  strength  in  coil  B  was  changed, 
the  pull  varied  directly  with  the  current  in  coil  B. 

Referring  to  Fig.  33,  it  is  seen  that  for  the  rim  sole- 
noids, 27=Z=2.54  cm.  in  each  case.  The  values  of 
ra  are  5.1,  7.6,  10.2,  and  12.7  cm.,  respectively. 

By  using  the  formula  6S  =  —  (60),  the  following  re- 


suits  are  obtained  : 

5.1 

7.6 
10.2 
12.7 


Os 

0.498 
0.334 
0.248 
0.200 


58 


SOLENOIDS 


Now  the  pull  due  to  a  solenoid  on  its  plunger  is 
directly  proportional  to  the  strength  of  the  current  after 
the  plunger  is  saturated.  Figure  36  shows  the  relative 
pulls  with  varying  degrees  of  excitation  in  the  rim 
solenoids,  and  Fig.  37  shows  the  results  of  the  test  of 
the  disk  solenoids. 


/  2  3 

RILO  IN 

FIG.  30.  —  Characteristics  of  Kim  Solenoids. 

Comparing   the   pull   P    (in     kilograms),  for   1500 

ampere-turns  in  each  case,  with  the  calculated  Os  values: 

e>                 P  £ 

5.1       .       .        0.498       .       .        2.16       .  .        3.48 

7.6       .       .        0.334       .       .        1.45       .  .        3.42 

10.2       .       .        0.248        .       .        1.08       .  .        3.30 

12.7                      0.200                      0.85  3.22 


THE   SOLENOID 


59 


It  will  be  observed  that  the  ratios  between  6S  and  P 
vary  slightly,  the  relative  pulls  being  greater  for  small 
values  of  ra.  This  is  due  to  the  effect  of  SB  in  the  coil 
used  to  saturate  the  iron  core  or  plunger. 


10 


8 


/  2  3  4  S  6 

KILO  IN 

FIG.  37.  —  Characteristics  of  Disk  Solenoids. 

The  curve  from  a  to  I  in  Fig.  38  is  plotted  from 
Fig.  36,  the  points  being  taken  from  the  pulls  corre- 
sponding to  the  different  mean  magnetic  radii  on  the 
ordinate  representing  6000  ampere-turns. 


60 


SOLENOIDS 


The  rim  windings  were  so  dimensioned  that  when 
telescoped  (theoretically),  they  would  form  a  disk  wind- 
ing, as  in  Fig.  39.  Now  the  sum  of  the  pulls,  in 
kilograms,  due  to  the  four  rim  windings,  with  1500 


/O 


V 


/O 


¥IG.  38.  —  Ratio  of  rm  to  Pull  for  Rim  and  Disk  Solenoids. 

ampere-turns  in  each  winding,  making  a  total  of  6000 
ampere-turns,  is  2.16  +  1.45  +  1.08  4-  0.85  =  5.54  kg. 

The  mean  magnetic  radius,  rm,  of  the  disk  winding 
consisting  of  the  telescoped  rim  windings  is,  according 
to  (53), 

4(5.1x7.6x10.2x12.7) 

,    ..x  7.6  x  10.2)+  (7.6  x  10.2  x  1±7)H- 

(10.2  x  12.7  x  5.1)  +  (12.7  x  5.1  x  7.6) 


THE   SOLENOID 


61 


Hence,  since  there  are  four  sec- 
tions, 

p  _4X_4  x2.54_1  97 
s~  rm  =         8 

Referring  again  to  Fig.  38,  it  is 
seen  that  when  rm  =  8,  P=5.54, 
which  coincides  with  the  results  ob- 
tained with  the  rim  windings. 

By  calculating  the  values  of  rm  for 
the  disk  windings  after  this  manner, 
the  rest  of  the  curve  a-c  is  obtained, 
which  coincides  with,  and  forms  a 
continuation  of,  the  curve  represent- 
ing the  test  of  the  rim  windings. 

The  curve  in  Fig.  40  represents 
the  product  of  the  pulls  multiplied 
by  the  mean  magnetic  radii,  the 
products  below  rm=  3  being  assumed 
from  the  natural  slope  of  the  curve. 

33.    MAGNETIC  FIELD  OF  PRAC- 
TICAL SOLENOIDS 

In  order  to  actually  see,  so  to 
speak,  just  what  relation  exists  be- 
tween the  lines  of  force  due  to  the 
current  in  the  coil  and  the  lines  of 
induction  in  the  plunger,*  the  author 
made  the  photographs  shown  in 
Figs.  41  to  44,  by  placing  the  sole- 
noid and  plunger  in  hard  sand,  so 

*  Electrical  World  and  Engineer,  Vol. 
XV,  1905,  p.  797. 


&.54CJH& 


FIG.  39.  —  Rim  Solenoids 
telescoped  to  form  Disk 
Solenoid. 


62 


SOLENOIDS 


that  the  plane  of  the  surface  of  the  sand  cut  the  center 
of  the  solenoid  and  plunger.     The  solenoid  was  then 


3S 


30 


20 


/O 


10 


FIG.  40.  —  Product  of  Pull  and  Mean  Magnetic  Radius. 

excited  and  iron  filings  sprinkled  on  to  show  the  flux 
paths.       The    solenoid    was    equally    excited    in    each 


case. 


THE   SOLENOID 


63 


In  Fig.  41  the  end  of  the  core  is  flush  with  the  end 
of  the  winding.  It  will  be  observed  that  the  field 
about  the  solenoid  is  very 
weak,  and  furthermore 
that  the  iron  plunger  ap- 
pears to  have  but  one  polar 
region,  i.e.  the  lines  of 
force  appear  to  leave  it 
uniformly  above  the  mouth 
of  the  solenoid.  Hence, 
the  polar  region  at  the 
mouth  of  the  solenoid  must 
be  very  small  indeed. 

Figure  42  shows  the 
plunger  inserted  one  third 
of  its  length  into  the  wind- 
ing. The  magnetic  field 


is  greatly  increased,  due  to 


FIG.  41.  —  Plunger  removed  from 
Solenoid. 


FIG.  42.  —  Plunger  inserted  one  third 
into  Solenoid. 


the  induction  in  the  iron. 
It  is  very  evident  that 
there  is  a  well-defined  pole 
within  the  solenoid,  but 
the  lines  of  force  leave  the 
projecting  portion  of  the 
plunger  uniformly,  indi-. 
eating  that  the  polar 
region  is  widely  distrib- 
uted. 

The  same  general  con- 
ditions exist  in  Fig.  43  as 
in  Fig.  42,  with  the  excep- 
tion that,  as  the  plunger  is 
•two   thirds   of   its   length 


64 


SOLENOIDS 


within  the  solenoid,  the  field  about  the  solenoid  is 
stronger,  and  the  polar  surface  of  the  plunger  protrud- 
ing from  the  solenoid  is 
smaller. 

The  general  character- 
istics of  the  bar  permanent 
magnet  are  met,  however, 
when  the  plunger  is  en- 
tirely within  the  solenoid, 
as  in  Fig.  44.  Here  the 
plunger  will  remain  at  rest, 
and  if  forcibly  moved  in 
either  direction,  it  will 
return  to  its  position  of 
equilibrium. 

Referring  again  to  Figs. 
42  and  43,  it  is  evident 
that  the  position  of  maxi- 


FIG.  43.  —  Plunger  inserted  two 
thirds  into  Solenoid. 

mum  pull  will  be  at  a 
point  between  the  posi- 
tions shown,  and  such  is 
the  case  for  solenoids  of 
the  general  dimensions 
of  the  one  in  question, 
while  for  very  short  sole- 
noids, and  for  low-flux 
densities  in  the  plungers, 
the  position  of  maximum 
pull  may  not  be  reached 
until  the  end  of  the 
plunger  has  protruded  a 
short  distance-  from  the 
solenoid. 


FIG.  44.  —  Plunger  entirely  within 
the  Solenoid. 


THE   SOLENOID  65 

34.    RATIO  OF  LENGTH  TO  AVERAGE  RADIUS 

By  building  up  (theoretically)  coils  of  various 
lengths,  average  radii,  and  thicknesses  from  the  for- 
mula given,  the  relations  between  the  above  dimensions 
may  be  investigated. 

Figure  45  shows  the  values  of  Ot  for  various  values  of 
ra  and  L  when  T=  1. 

It  will  be  remembered  that  6t  is  the  force  at  the 
center  of  the  entire  coil  for  one  centimeter  of  length, 
regardless  of  the  thickness  of  the  winding,  since 


(56) 


Hence,  if  the  value  of  6t  may  be  determined  for 
coils  of  any  dimensions,  the  magnetizing  force  at  the 
center  of  the  coil  will  be  86=  0.27rZZV<9,  (61).  (See 
p.  42.) 

In  Fig.  46  is  shown  the  effect  of  changing  the  thick- 
ness of  the  winding.  It  will  be  seen  that  there  is  a 
slight  variation  in  the  values  of  6t  for  given  values  of 
ra  and  L,  for  small  values  of  ra,  but  that  the  difference 
for  relatively  large  values  of  ra  is  inappreciable. 

It  will  also  be  noticed  from  the  slope  of  the  curve 
for  ra  =  1,  that  the  value  of  6t  gradually  approaches 
2,  which  value  it  can  never  exceed  in  any  coil  when 
0.27rZZV=l,  which  is  the  basis  upon  which  these  cal- 
culations have  been  made. 

Referring  again  to  Fig.  46,  it  will  be  observed  that 
for  coils  of  one  centimeter  length  the  relation  is  ap- 
proximately 

*,  =  -,  (59) 


©t      /.O 


FIG.  45.  —  Force  due  to  Solenoids  with  Unit  Thickness  or  Depth  of 
Winding. 


0 


8  /O 


FIG.  46.  —  Effect  of  changing  Thickness  of  Winding. 


68  SOLENOIDS 

when  #4=1  or  less,  while  for  the  same  values  of  0t, 

0,  =  ^f  C62) 

(approximately),  when  L  exceeds  5. 

The  value  of  0t  above  0t  =  1  may  be  expressed  with  a 
fair  degree  of  accuracy  by  the  empirical  formula 

A  O  i     ft  S  R  Q  \ 

'         loTl' 

It  is  obvious  that  the  value  of  fy,  as  given  in  (63), 
will  constantly  decrease  as  the  length  of  the  winding 
increases.  Hence,  for  a  very  long  solenoid  of  small 
radius,  Ot  =  2. 

In  practice  the  total  ampere-turns  are  calculated 
direct  for  the  entire  coil.  (See  p.  34.)  Hence,  to  de- 
termine the  ampere-turns  per  centimeter  length,  the 
total  ampere-turns  must  be  divided  by  the  length  of 
the  winding.  Therefore, 


(64) 

±J 

and  when  0t  =  2, 


which  is  the  formula  for  a  very  long  solenoid  of  small 
radius,  or  for  a  coil  whose  core  forms  a  closed  ring. 

Formula  (65)  is  simply  the  m.  m.  f.,  which  is  always 
C9=  0.47rZZV,  divided  by  the  length  of  the  winding 
which,  in  the  two  cases  mentioned  above,  represents  the 
mean  length  lm  of  the  magnetic  circuit. 


CHAPTER   VI 

PRACTICAL  SOLENOIDS 

35.    TESTS  OF  PRACTICAL  SOLENOIDS 

IN  order  to  obtain  practical  data  on  the  action  of 
solenoids,  the  author  made  numerous  tests*  of  solenoids 
of  various  dimensions.  Five  solenoids  were  con- 
structed, each  having  an  average  radius  of  2.76  cm., 
while  the  lengths  were  7.63,  15.25,  22.8,  30.5,  and  45.8 
cm.,  respectively. 


FIG.  47. —  Testing  Apparatus. 

For  the  purpose  of  determining  the  actual  pulls  due 
to  varying  degrees  of  excitation  of  the  solenoids,  the 
apparatus  illustrated  in  Fig.  47  was  employed.  The 
plunger  was  attached  to  the  scales  and  the  counter- 
weight adjusted  so  that  the  weight  of  the  plunger  was 

*  Electrical  World  and  Engineer,  Vol.  XLV,  1905,  pp.  796-799. 

69 


70    '  SOLENOIDS 

counterbalanced,  and  the  scales  balanced  at  zero. 
Hence,  the  weight  of  the  plunger  was  entirely  elimi- 
nated. 

By  means  of  an  adjustable  rheostat  and  an  ammeter, 
any  desired  current  strength  was  readily  obtainable, 
and  since  the  turns  of  each  solenoid  were  known,  the 
ampere-turns  were  easily  determined. 

The  plunger  used  in  this  particular  test  was  the  same 
one  used  in  the  tests  of  the  rim  and  disk  solenoids  and 
consisted  of  a  Swedish  iron  bar  1  m.  long  and  2.87 
cm.  in  diameter,  making  its  cross-sectional  area  6.45 
sq.  cm. 

The  reason  for  using  coils  and  plungers  of  miscel- 
laneous dimensions  was  due  to  the  fact  that  these  were 
stock  sizes,  but  it  will  be  seen  that  the  lengths  of  the 
solenoids  bear  a  constant  relation  to  one  another,  and 
all  have  the  same  average  radius. 

Figure  48  shows  the  result  of  such  a  test.  The 
curve  marked  L  =  2.54,  ra  =  3,  is  the  smaller  of  the  disk 
windings  shown  in  Fig.  34,  p.  56.  It  will  be  ob- 
served that  the  relation  between  the  pull  and  ampere- 
turns  for  the  shorter  solenoid  is  not  a  straight-line 
proportion  until  approximately  6000  ampere-turns  have 
been  developed  in  the  winding. 

It  will  be  seen  that  by  drawing  straight  lines  from 
the  origin,  and  parallel  to  the  curves  in  Fig.  48,  the 
straight  lines  would  represent  the  ampere-turns  required 
to  produce  the  pulls  indicated,  if  the  plunger  was 
already  saturated. 

Referring  to  Fig.  37,  p.  59,  the  pull  due  to  the  L  — 
2.54,  ra=3  solenoid  on  the  separately  magnetized 
plunger  is  12.2  kg.  for  6000  ampere-turns.  Now,  in  Fig. 
48,  the  ampere-turns  required  for  the  same  pull  are  ap- 


PRACTICAL   SOLENOIDS 


71 


proximately  9000.      Hence,  it  is  evident  that  9000  — 
6000  =  3000  ampere-turns  are  expended  in  keeping  the 


IO 


J5 


2O 


35 


25          30 
KILO  IN 

FIG.  48.  —  Maximum  Pulls  due  to  Practical  Solenoids  of  Various 
Dimensions. 

plunger  saturated.  An  examination  of  the  other  curves 
in  Fig.  48  shows  similar  losses,  though  less  marked  as 
the  length  increases. 

In  these  tests  the  maximum  pull  was  taken  in  each 
case,  and  since  the  position  of  maximum  pull  inside  the 
solenoid  changes  its  position  with  the  induction  in  the 
plunger,  it  will  be  seen  that  the  curves  in  Fig.  48  do 
not  necessarily  represent  the  pulls  at  the  exact  center 
of  the  solenoid. 


72 


SOLENOIDS 


This  will  be  understood  by  an  examination  of  Figs. 
49  and  50  which  show  the  pulls  corresponding  to  differ- 


/S 

17 
/G 

15 
H 
13 
/2 

^     " 
tn 

^     10 

I   9 

I  8 
7 
6 

S 

4 
3 
2 


I 


L 


KILO  /A/ 

FIG.  49.  —  Effect  of  Varyiug  Position  of  Plunger  in  Solenoid. 

ent  degrees  of  excitation  expressed  as  kilo  ampere-turns 
(thousands   ampere-turns).      These   are   the  i  =  15.3, 


i  O 


6 
8 
JO 
12 

/6 

/e 
20 


30 
32 
34 
36 
38 
10 


PULL 


1 


\ 


XI  \ 


\ 


\ 


\ 


\ 


74 


SOLENOIDS 


ra=  2.76,  and  L  =  30.5,  ra=  2.76,  solenoids  referred  to 
in  Fig.  48. 

In  Fig.  49  the  curves  are  for  the  following  positions 
of  the  end  of  the  plunger : 


CURVE 

POSITION  OK  PLUNGER  IN  COIL 

1 

1 

2 

I 

3 

A 

4 

1 

5 

& 

6 

f 

7 

1 

8 

t 

9 

even  with  farther  end 

10 

projecting  2.5  cm. 

In  Fig.  50  the  positions  are: 

CUKTB 

POSITION  OF  PLUNGER  IN  COIL 

1 

even  with  end 

2 

i 

0 

3 

I 

4 

T52 

5 

1 

6 

A 

7 

1 

8 

I 

9 

5 

10 

even  with  farther  end 

11 

projecting  2.5  cm. 

It  will  be  observed  that  the  curves  representing  the 
relation  between  pull  and  ampere-turns  before  the 
plunger  reaches  the  center  of  the  winding  have  charac- 


PRACTICAL   SOLENOIDS  75 

teristics  similar  to  the  curves  in  Fig.  48,  i.e.  the  straight 
portions  of  the  curves  do  not  point  to  the  origin,  but  to 
points  representing  the  ampere-turns  required  to  satu- 
rate the  core.  These  tests  were  also  made  with  the 
plunger  of  6.45  sq.  cm.  area,  and  1  m.  in  length. 

36.    CALCULATION  OF  MAXIMUM  PULL  DUE  TO 
SOLENOID 

It  has  been  stated  that  a  solenoid  will  attract  its 
plunger  within  itself  until,  if  the  plunger  be  the  same 
length  as  the  solenoid,  the  ends  of  the  plunger  will  be 
even  with  the  ends  of  the  winding.  Some  characteris- 
tics will  be  shown  presently.  If  now  another  plunger, 
exactly  similar  to  the  first,  be  held  near  one  of  the  ends 
of  the  first  plunger,  end  to  end,  it  will  be  attracted 
to  the  first  plunger,  and  then  the  two  will  be  drawn 
inside  the  winding  until  the  outer  ends  are  equidistant 
from  the  ends  of  the  coil,  barring  friction,  of  course. 
This  shows  plainly  that  a  plunger  longer  than  the 
winding  increases  the  range  of,  and,  consequently,  the 
work  due  to,  a  solenoid. 

It  has  been  found  mathematically,  and  confirmed  by 
experiment,  that  the  force  required  to  separate  the  two 
plungers,  in  a  long  solenoid,  under  these  conditions, 
that  is,  when  the  abutting  ends  are  exactly  at  the 
center  of  the  winding,  and  are  perfectly  joined  mag- 
netically, is 

-P-  =  f^,  (66) 

O  7T 

wherein  Pd  is  the  pull  in  dynes  and  <~B  is  the  magnetic 
induction  in  the  plunger. 


76  SOLENOIDS 

Since  1  gram  =  981  dynes,  the  pull  in  grams  may 
be  expressed 


p  67 

9      87TX981 

In  this  book  the  unit  of  pull  will  be  the  kilogram 
(1000  grams).  Representing  this  by  P, 

p  —         $¥A  ,gg. 

8?r  x  981,000' 

In  the  case  of  the  simple  solenoid,  when  the  plunger 
reaches  its  position  of  maximum  pull,  the  attraction 
will  not  be  between  two  parallel  faces  of  iron,  or  rather 
the  flux  in  the  two  pieces  of  iron,  but  between  the 
magnetizing  force,  or  intensity  of  magnetic  field  SB) 
and  the  induction  68  in  the  plunger. 

The  intensity  of  magnetic  field  at  the  center  of  a 
solenoid  of  reasonable  length  is  practically  the  same 
whether  the  latter  is  surrounded  by  iron  or  air. 

Now,  <£  =  !p  (34) 

crb 

wherein  $  is  the  flux,  £f  the  m.  m.  f.,  and  G&  the  reluc- 
tance. 

<^  =  -^  (37) 

A.fjb 

wherein  lm  is  the  mean  length  of  the  magnetic  circuit 
under  consideration,  and  yu,  the  permeability  which,  for 
air,  is  unity. 

Now,  practically  all  of  the  reluctance  in  the  magnetic 
circuit  of  a  solenoid  with  an  air-core  is  in  the  air  core 
itself,  for  there  the  lines  of  force  are  confined  to  a  lim- 
ited channel.  While  the  mean  length  of  that  portion 
of  the  magnetic  circuit  outside  of  the  coil  is  somewhat 
greater,  for  solenoids  of  average  proportions,  than  that 


PRACTICAL  SOLENOIDS  77 

of  the  air-core  within  the  winding,  its  cross-section  is 
practically  infinite.  Hence,  the  ratio  of  external  to 
internal  reluctance  is  very  small  indeed. 

When,  however,  an  iron-core  is  substituted  for  the 
air-core,  the  external  reluctance  may  exceed  the  inter- 
nal, providing,  of  course,  that  the  external  circuit  con- 
tains no  magnetic  material. 

Now,  since  the  intensity  of  the  magnetic  field  is 
maximum  at  the  center  of  a  solenoid,  it  is  natural  to 
assume  that  the  pull  due  to  a  coil-and-plunger  will  be 
maximum  when  the  end  of  the  plunger  is  at  or  near 
the  center  of  the  coil.  As  a  matter  of  fact,  such  is  the 
case  when  the  plunger  is  saturated. 

~ 


FIG.  51.  —  Solenoid  Core  consisting  of  one-half  Air, 
and  one-half  Iron. 

The  conditions,  then,  are  as  shown  in  Fig.  51.     Here 

^  =  Z2  =  —  .    From  the  table,  p.  30,  it  will  be  seen  that 

2* 

when  the  plunger  is  saturated,  ££>  =  20,000  approxi- 
mately. Hence,  if  it  is  assumed  that  the  cross-sec- 
tional area  of  the  plunger  is  1,  then  c/>  =  £&A  =  20,000. 
From  the  table,  p.  323,  it  is  seen  that  for  wrought  iron, 
when  68  =  20,000,  ft  =  100  approximately. 

Now,  &t>~-?-i  or  the  sum  of  all  the  separate  reluc- 


tances.    (See  p.  33.)     Hence,  in  this  case  (neglecting 
the  external  reluctance), 


78  SOLENOIDS 

wherein  ^  and  />t2  represent  the  permeabilities  of  the 
air-core  and  iron-core  corresponding  to  ^  and  12.     Con- 

sequently, /AJ  =  1,  /JL2  =  100. 

But  Z1==Z2  =  |,  and  4  =  1. 

Hence, 


2/*j     2/45,      2      200  200  200    ~1~98* 

If   the    plunger  was   not   thoroughly  saturated,  the 
permeability  would  be  higher,  say  1000  ;   in  which  case 

the  reluctance  would  be  practically  c/£>  =  —  • 


Now,  6B  =  i&S  (42),  and  B6  =  .  (64) 

Lt 

Hence, 

SB  =  M^HA  (70) 

L 

Since  6B  represents  the  flux  per  square  centimeter  or 
unit  area,  (TO)  may  be  written, 


and  since,  for  the  position  of  maximum  pull,  ^  =  —  , 


(72) 


for  this  position. 

Now  the  value  of  6B  at  the  saturation  point  is  20,000. 
Consequently, 

£&  =°-47rZZVr^  x  20,000.  (73) 


PRACTICAL   SOLENOIDS  79 

Substituting  the  value  of  662  from  .(73)  in  (68), 

p  =  2®BOfrx  0.4  TtIN0tA\ 
STT  x  981,000  L 


P  =  .  (74) 


This  value,  68  =  20,000,  will  be  assumed  in  all  future 
calculations  of  the  solenoid  for  thoroughly  saturated 
plungers  of  soft  iron  or  steel. 

37.   AMPERE-TURNS   REQUIRED  TO   SATURATE 
PLUNGER 

In  (74)  the  losses  due  to  the  ampere-turns  required 
to  keep  the  plunger  saturated  have  not  been  consid- 
ered. These  must  be  allowed  for  in  solenoids  up  to  25 
or  30  cm.  in  length,  but  for  greater  lengths,  the  losses 
are  inappreciable. 

Assigning  X  to  this  loss,  (74)  becomes 

(75) 

as  the  loss  will  vary  with  the  cross-sectional  area  of  the 
plunger  for  the  same  ampere-turns. 

In  Fig.  52  are  shown  the  approximate  values  of  X  as 
taken  by  observation  from  tests. 

From  (75) 

7^=  ?  l^L  +  A\,  (76) 

and  since 

0t=2 ^—  (approx.),  (63) 

(76)  may  be  written 

IN=     ,981Pf    x-Mx-  (T7> 

'n 
1.07  L, 


A  lo          T(l 
yi     —  — 


80 


SOLENOIDS 


This  formula  will  be  found  quite  accurate,  but  it  is 
well  to  increase  the  calculated  ampere-turns,  to  allow 


400 


BOO 


/OO 


5  /O  /5          2O          25         3O 

/.    CC/M  s.^ 

FIG.  52.  —  Approximate  Ampere-turns  required 
to  saturate  Plunger. 

for  variation  in  the  value  of  <EB  in  the  plunger,  and  since 
the  ampere-turns  decrease  with  a  rise  in  temperature 
of  the  winding  of  the  solenoid,  for  a  given  e.m.  f.,  it  is 
always  better  to  have  a  little  too  much  pull  than  not 
quite  enough. 

The  weight  of  the  plunger,  as  well  as  losses  due  to 
friction,  should  be  allowed  for,  according  to  the  condi- 
tions under  which  the  solenoid  is  to  be  operated,  since 
in  the  formula?  the  weight  of  the  plunger  is  not  consid- 
ered, and  in  the  tests  referred  to,  the  plunger  was 
counterbalanced. 

Substituting  the  value  of  6t  from  (63)  in  (74), 


P  — 


981 L 


(78) 


PULL 


82  SOLENOIDS 

Figure  53  is  the  result  of  a  test  of  a  solenoid  of  the 
following  dimensions  :  L  =  25.4,  ra  =  6.8,  T=  8.6.  The 
plunger  was  of  soft  steel  17.9  sq.  cm.  in  area  and  60 
cm.  long.  In  this  as  was  the  case  with  all  the  sole- 
noids tested  (the  rim  solenoids  excepted),  the  internal 
diameter  of  the  solenoid  was  made  as  small  as  possible; 
the  brass  tube,  insulation,  and  sufficient  freedom  for  the 
plunger  being  the  controlling  factors. 

The  values  in  Fig.  53  compare  very  favorably  with 
values  calculated  by  the  above  formulas. 

38.    RELATION  BETWEEN   DIMENSIONS  OF   COIL 
AND   PLUNGER 

The  general  construction  of  the  solenoid  may  vary 
with  the  ideas  of  the  designer,  but  the  dimensions  of  the 
winding  and  plunger  are  all  important,  and  it  must  be 
remembered  that  the  strength  of  a  solenoid  is  limited 
by  the  carrying  capacity  of  the  winding.  / 

As  the  total  work  obtained  from  any  long  solenoid  is 
practically  constant,  regardless  of  its  actual  length,  for 
the  same  ampere-turns,  the  pull  for  any  long  solenoid 
is  proportional  to  the  ampere-turns  per  unit  length. 
Therefore,  a  50-cm.  solenoid  will  have  practically  the 
same  pull  as  a  25-cm.  solenoid,  if  twice  the  energy  is  ap- 
plied to  the  winding. 

The  diameter  of  the  solenoid  will  vary  with  the  di- 
ameter of  the  core  or  plunger,  and  other  conditions, 
such  as  heating,  etc.,  but  a  good  general  rule  is  to 
assume  a  diameter  for  the  solenoid  equal  to  about  three 
times  the  diameter  of  the  plunger. 

An  examination  of  Fig.  48  will  show  that  the  ampere- 
turns  per  square  centimeter  of  core  should  never  fall 


PRACTICAL   SOLENOIDS  83 

below  1000  for  the  shorter  solenoids,  in  order  to  keep 
the  core  well  saturated.  Furthermore,  it  is  desirable 
to  work  the  cores  of  solenoids  at  high  densities  because 
of  the  relative  weight  of  the  plunger  when  working  with 
lower  densities,  and  the  pull  per  ampere-turn  is  much 
less  at  low  densities.  If  the  core  was  not  saturated,  the 
pull  would  not  be  directly  proportional  to  the  ampere- 
turns,  as  the  permeability  of  the  iron  would  be  very 
changeable  at  low  densities. 

On  the  other  hand,  it  is  not  economical  to  have  more 
ampere-turns  than  are  necessary  to  saturate  the  plunger. 
Hence,  the  following  method  may  be  adopted. 

Let  INA  =  the  product  of  the  minimum  ampere-turns 
and  the  minimum  cross-sectional  area  of  the  plunger 
necessary  to  keep  the  plunger  saturated  and  produce 
the  required  pull,  ZZVc=the  minimum  ampere-turns 
per  square  centimeter  of  plunger  Avhen  the  latter  is  satu- 
rated, and  A  =  cross-sectional  area  of.  the  plunger  in 
square  centimeters.  Then, 

(79) 

and  INA  =  INCAZ  (80).  This  will  be  understood  by 
referring  to  Fig.  54. 

^4.s  an  example,  assume  that  INC  =  1000,  which  is  a 
good  average  value  to  use  in  practice.  Then  INA  = 
1000  A\  whence 


OOO        31.6 

By  this  method  the  ampere-turns  will  always  be 
1000  for  each  square  centimeter  of  plunger,  which 
insures  the  minimum  expenditure  in  watts  to  produce 
a  given  result. 


84 


SOLENOIDS 


As  before  stated,  other  values  than  INC=  1000  may 
be  chosen,  but  as  the  solenoids  in  common  use  are  not 


360 


320 


-200 


IO  12 


16  IQ 


A   (so  CMS) 

FIG.  54.  —  Ratio  between  Ampere-turns  and  Cross-sectional  Area  of 
Plunger. 

very  great  in  length,  the  author  has  found  the  above 
value  to  be  approximately  correct  for  general  practice, 
although  INC  =  1250  is  a  safer  value. 

Since  A=  dp2  x  0.7854  (81),  the  diameter  of  the 
plunger  dp  may  be  calculated  direct  by  substituting  the 
value  of  A  from  (81)  in  (80).  Then, 

IN  A  =  0.617  INcdp\  (82) 


and 


dp  = 


INA 


I.617ZZV1 


(83) 


PRACTICAL   SOLENOIDS  85 

(84) 


T-,  T     0.617       c  /  Q  r  N 

Hence,  IN=-  c-^-  ,  (85) 


or  iar=    '-      "  =  0.7854  JV^/.  (86) 


and 


which  means,  of  course,  that  the  ampere-turns  will  be 
INe  times  the  cross-sectional  area  of  the  plunger. 

For  short  solenoids,  IN—  A\  must  be  substituted  for 
ZZV,  but,  in  general,  the  above  method  is  near  enough. 

39.   RELATION  OF    PULL    TO  POSITION  OF    PLUNGER 
IN  SOLENOID 

It  was  stated  that  when  the  end  of  the  plunger  enters 
the  solenoid,  the  pull  increases  until  the  position  of 
maximum  pull  is  reached,  when  it  again  falls  off  until, 
if  the  plunger  be  the  same  length  as  the  solenoid,  the 
pull  will  fall  to  zero  when  the  ends  of  the  former  are 
even  with  those  of  the  latter,  while  if  the  plunger  be 
longer  than  the  solenoid,  the  end  of  the  plunger  will 
protrude  a  short  distance  from  the  solenoid. 

Figures  55  to  58  show  the  characteristics  of  the  sole- 
noids of  constant  radius  (ra  =  2.76)  and  lengths  15.3, 
22.8,  30.5,  and  45.8  cm.,  respectively,  with  the  plunger 
1  m.  in  length,  and  6.45  sq.  cm.  in  cross-section. 

It  will  be  observed  that  as  the  length  increases,  the 
pull  is  more  uniform  over  a  given  distance,  and  that 
by  assuming  a  pull  lower  than  the  actual  pull,  the 
range  may  be  somewhat  increased. 


PULL 


88 


SOLENOIDS 


In  Fig.  59  is  shown  the  characteristics  of  the  45.8- 

cm.  solenoid  with  a  plunger  of  the  same  length  as  the 

IP 


PLUNGER  IN 

FIG.  59.  —  Characteristics  of  45.8-cm.   Solenoid   with  Plunger  of  Same 

Length. 

solenoid.  It  will  be  noticed  that  a  greater  range  of 
action  may  be  obtained  with  a  plunger  longer  than  the 
solenoid,  and  that  the  range  increases  with  the  ampere- 
turns.  This  latter  effect  is  due  to  the  fact  that  the 
ratio  of  total  ampere-turns  to  those  required  to  saturate 
the  plunger  is  greater  for  large  values  of  IN. 

The  pull,  however,  will  not   be  so  great  where  the 


PRACTICAL   SOLENOIDS 


89 


en  00 


yj  £ 


l*J  to 
U'5 

^^ 

3  § 
S| 

o 
I 

8 


90 


SOLENOIDS 


plungers  are  the  same  length  as  the  coils,  excepting  in 
cases  of  comparatively  long  solenoids. 

In  Fig.  60  are  shown  the  force  curves  due  to  the  25.4- 
cm.  solenoid  previously  referred  to.     This  is  plotted 

0.6 


PLUNGER  IN  COIL 

FIG.  61. —  Characteristics  of  Solenoid  8  cms.  long. 

from  Fig.  53.     The  curves  in  Fig.  61  are  due  to  a  sole- 
noid 8  cm.  long,  with  a  soft  steel  plunger  1  sq.  cm.   in 


PRACTICAL   SOLENOIDS 


91 


cross-section,  and  30  cm.  long.     The  other  dimensions 
are  T=  2,  ra  =1.09. 
/.o 


0.5 


5  10 

PLUNGER  IN  COIL 

FIG.  G2.  — Characteristics  of  Solenoid  15  cms.  loni;. 


25 


20 


I     ,5 


-  l5,OOc 


,c  10,000 


15 


PLUNGER  I  A/  COIL 

FIG.  G3.  —  Characteristics  of  Solenoid  17.8  cms.  long. 


/5 


92 


SOLENOIDS 


The  characteristics  due  to  a  solenoid  in  which  L  =  15, 
^=1.17,  and  ra  =  0.66,  are  shown  in  Fig.  62.  The 
plunger  was  1.27  sq.  cm.  in  cross-section. 

Figure  63  is  due  to  a  solenoid  of  dimensions  L  =  17.8, 
T  =  2.54,  ra  =  3.5.  The  sectional  area  of  the  plunger 
was  11.4  sq.  cm.  and  the  length  25.4  cm. 

The  above  cases  are  mentioned  at  random  in  order  to 
show  the  general  relations  existing  between  solenoids 
of  all  dimensions.  The  maximum  pulls  for  any  of 
these  solenoids  may  be  closely  approximated  by  use 
of  formula  (78). 


-J 

-J 

CL 


x 

^c 


PERCENT  LENGTH  OF  COIL 

Fia.  G4.  — -  Effect  of  increased  m.m.f.  on  Range  of  Solenoid. 


PRACTICAL   SOLENOIDS 


93 


40.  CALCULATION  OF  THE  PULL  CURVE 

A  comparison  of  the  curves  in  Figs.  55  to  63  with 
the  theoretical  force  curve  in  Fig.  28  will  show  that, 
while  there  is  a  resemblance,  the  position  of  maximum 
pull  is  shifted  toward  the  farther  end  of  the  solenoid 
for  very  weak  magnetizing  forces,  while  the  theoretical 
force  curve  is  the  same  at  both  sides  of  the  vertical 
center  of  the  solenoid. 

This  is  due  to  the  fact  that  for  magnetizing  forces  of 
low  value  the  plunger  may  not  become  saturated  until 


30 


35 


-=70 


PLUNGER  /A/  COIL,  <c/ws.) 

FIG.  65.  —  Comparison  of  Solenoids  of  Constant  Radii,  but  of  Different 

Lengths. 


94 


SOLENOIDS 


PRACTICAL    SOLENOIDS  95 

it  has  protruded  a  short  distance  from  the  farther  end 
of  the  solenoid.  Figure  64,  in  particular,  shows  this 
effect,  which  is  plotted  from  Fig.  53.  In  these,  how- 
ever, the  plunger  has  become  saturated  before  it  has 
reached  the  farther  end  of  the  solenoid,  owing  to  suffi- 
cient magnetizing  force  to  saturate  the  plunger. 

It  can  be  shown  that,  in  general,  the  curves  of  all 
solenoids  are  very  similar  for  equal  degrees  of  magnet- 
ization. 

In  Fig.  65  are  shown  curves  due  to  the  solenoids  of 
constant  radius  (ra  =  2.76)  and  of  lengths  15.3,  22.8, 
30.5,  and  45.8  cm.,  respectively,  tested  with  the  plunger 
one  meter  in  length,  and  with  15,000  ampere-turns. 
The  plunger  was  thoroughly  saturated,  since  the  ampere- 
turns  per  square  centimeter  of  core  were  2300. 

By  grouping  the  curves  in  Fig.  65  on  a  common 
plane,  so  as  to  make  the  ampere-turns  per  unit  length 
the  same  in  all  cases  (see  Fig.  66),  it  is  seen  that  the 
curves  are  similar,  with  the  exception  that  the  peaks 
are  proportionately  higher  for  the  longer  solenoids.  If, 
however,  the  pulls  throughout  the  entire  range  of  each 
curve  in  Fig.  66  are  compared  with  the  maximum  pull 
for  that  solenoid,  the  curves  are  found  to  be  practically 
similar  in  all  cases  cited.  This  common  curve  is  illus- 
trated in  Fig.  67. 

It,  therefore,  remains  to  determine  the  equation  for 
this  curve,  which  is  partly  sinusoidal,  and  the  equation 
y  =  sin  0.77  a;  (88)  satisfies  this  condition  for  practical 
purposes,  as  reference  to  Fig.  68  will  show.  In  this 
case  the  length  of  the  solenoid  is  compared  with  180 
degrees. 

While  the  solenoid  pull  curve  in  Fig.  68  is  slightly 
higher  than  the  y  =  sin  0.77  x  curve  from  25  degrees  to 


96 


SOLENOIDS 


120  degrees,  it  must  be  understood  that  the  percentage 

of  maximum  pull  throughout  the  first  half  of  the  sole- 

100 


I" 


I 


\ 


0         10        20        30        40        50        60         70        80        SW      100 

Per  Cent  Length  of  Solenoid 

FIG.  67.  —  Average  of  Curves. 

noid  is  greater  for  higher  than  for  lower  magnetizing 
forces,  owing  to  the  fact  that  the  plunger  is  more  quickly 


.« 

.s 

,7 
.6 

.5 
.4 

.3 
.2 
.1 

S 

^ 

^ 

^ 

^ 

L^^5j 

^ 

s> 

10U 
90 

V. 

.| 

-a 

w  = 

30  s 

20  K 
10 

m 

<&i 

^ 

S 

\ 

N> 

\ 

\ 

<f 

^ 

\ 

\ 

^s 

/ 

^ 

?/ 

\ 

X 

\ 

s 

// 

^ 

' 

\ 

\ 

/, 

^ 

/ 

\ 

\ 

w 

/ 

s 

\ 

\ 

/ 

'/ 

\ 

\ 

d 

y 

\\ 

Y 

\ 

1   10  30  30  40  51)  60  70  80  90  100  1LO  120  130  140  150  160  170  180 

Total  Length  of  Solenoid  Considered  as  ISODegrees 
FIG.  08.  —  Average  Solenoid  Curve  compared  with  Sinusoid. 


PRACTICAL   SOLENOIDS 


97 


saturated  under  the  former  condition,  thereby  increasing 
the  pull  —  or,  to  be  exact,  the  percentage  of  maximum 
pull ;  and  since  this  curve  represents  the  pull  due  to 
15,000  ampere-turns,  the  percentage  of  maximum  pull 
would  be  somewhat  lower  with  a  magnetizing  force 
just  sufficient  to  saturate  the  plunger  at  the  position  of 
maximum  pull,  and,  therefore,  the  curve  y  =  sin  0.77  x 
represents  a  good  average,  as  the  curves  beyond  the 
position  of  maximum  pull  do  not  vary  appreciably  as 
the  magnetizing  force  increases,  after  the  plunger  is 
saturated. 


10        20 


90      100 


30       40         50        60        70 
Per  Cent  Length  of  Solenoid 
FIG.  G9.  —  Effect  of  Increasing  Ampere-turns. 

This  effect  is  illustrated  in  Fig.  69,  which  is  the  result 
of  a  test  of  the  30.5-cm.  solenoid.  An  inspection  of  Fig. 
69  also  shows  that  the  range  of  the  solenoid  is  much 
greater  with  high  than  with  low  magnetizing  forces. 


98  SOLENOIDS 

Again  referring  to  Fig.  68,  the  dotted  curve  repre- 
sents the  effect  of  using  a  plunger  of  the  same  length 
as  the  solenoid,  in  the  case  of  a  long  solenoid. 

Now  from  these  data  a  curve  may  be  plotted  showing 
the  approximate  pull  at  all  points  throughout  the  range 
of  the  solenoid.  It  will  be  recalled  that  the  ratio  of  the 
actual  pull  to  the  maximum  (j/)  is  equal  to  sin  0.11  x  ; 
and  if  we  let  /2  represent  the  distance  in  centimeters, 
the  plunger  is  in  the  coil,  and  compare  the  linear  ratios 
with  those  represented  by  degrees,  we  have, 

(89) 

Representing  the  pull  at  any  point  by  JP,  the  ratio  of 
actual  to  maximum  pull  is 


T  n   .    138.6  L 

whence  p  =  P  sin  --  -  —  2.  (90) 

JL/ 


41.    POINTED  OR  CONED  PLUNGERS 

By  pointing  or  tapering  the  plunger,  varying  force 
curves  may  be  obtained,  the  pull  usually  being  maximum 
when  the  pointed  end  has  protruded  from  the  other  end 
of  the  coil  to  which  it  entered,  this  depending  upon  the 
amount  of  tapering. 

In  this  case,  however,  the  pull  is  not  so  great  as  with 
the  regular  plunger,  owing  to  the  diminished  cross-sec- 
tional area  of  the  iron  due  to  tapering. 

It  is  obvious  that  almost  any  desired  form  of  curve 
may  be  obtained  by  giving  the  plunger  peculiar  shapes. 


PRACTICAL   SOLENOIDS 


99 


42.    STOPPED  SOLENOIDS 

The  effective  range  of  a  solenoid 
may  be  greatly  increased  by  plac- 
ing a  piece  of  iron  at  the  farther 
end  of  the  solenoid.  This  is  com- 
monly called  a  Stop,  and  may  pro- 
ject within  the  winding  if  desired. 

Figure  70  shows  an  experimental 
solenoid*  designed  by  the  author 
for  tests  of  the  Stopped  Solenoid. 
The  extension  piece  on  the  end  is 
provided  with  a  thumbscrew  which 
permits  of  cores  of  various  lengths 
being  fastened  in  any  desired  posi- 
tion. 

In  the  tests  to  be  described,  all 
cores  were  of  soft  iron,  1.27  sq.  cm. 
cross-sectional  area,  and  in  each 
case  there  were  6800  ampere-turns 
in  the  winding.  The  dimensions  of 
the  coil  were  L  =  15,  ra  =  0.66  cm. 

Curve  a  in  Fig.  71  is  due  to  the 
attraction  between  the  magnetiz- 
ing force  in  the  coil  and  the  flux 
in  the  plunger,  which  was  15  cm. 
in  length.  Curve  b  was  obtained 
from  the  same  solenoid,  but  with  a 
stop  2.54  cm.  long,  its  right-hand 
end  being  even  with  the  right-hand 
end  of  the  winding.  Curve  <?  is 

*  American  Electrician,  Vol.  XVII, 
1905,  pp.  299-302. 


fi 

i 

i 

°o 

i 

§ 

» 
t 

1 

i 
i 
i 

i 
i 

i 
i 

1 
i 

I 

—  Experimental 

1 



i 

d 

i 

i 

i 

i 

i 

i 

6 

i 

i 

£ 

i 

i 

i 

i 

i 

i 

i 

i 

i 

i 
i 

i 

i 
i, 

i 

i 

i 

i 

1 

i 

i 
i 

1 

i 

ii 

i 

1 

i" 

i 

I 

i 

i 

i 

u 

fit 

k 

IfcaJ 

i 

100 


SOLENOIDS 


PRACTICAL  SOLENOIDS  101 

from  a  test  with  a  stop  of  approximately  the  same  length 
as  the  plunger,  and  with  its  right-hand  end  even  with  the 
left-hand  end  of  the  winding,  as  in  the  case  of  curve  b. 

It  is  obvious  that  a  single  piece  of  iron  at  the  end  of 
the  solenoid  is  beneficial,  as  it  prevents  the  pull  from 
falling  off  at  that  end,  thereby  increasing  the  effective 
range.  It  should  be  noted  that  all  parts  of  the  frame  of 
this  experimental  solenoid  were  of  non-magnetic  ma- 
terial, the  only  ferric  portions  being  the  plunger  and  stop. 

The  curves  c?,  e,f,  and  g  are  due  to  the  end  of  the  stop 
being  inserted  in  the  coil  one  sixth,  one  third,  one  half, 
and  two  thirds  of  the  length  of  the  solenoid,  respectively. 

An  examination  of  Fig.  71  shows  that  the  curves 
c,  d,  e,  etc.,  are  the  result  of  the  attraction  between  the 
plunger  and  the  stop  plus  the  solenoid  effect. 

It  will  be  noted  that  stronger  pulls  are  obtained  with 
the  long  stop  than  with  the  short  one.  This  is  due  to 
the  fact  that  the  longer  rod  offers  a  better  return  path 
for  the  lines  of  force,  thereby  increasing  the  induction 
and,  consequently,  the  pull. 

Thus  far  we  have  been  dealing  with  solenoids  which 
depend  upon  the  air  or  surrounding  region  as  a  return 
path  for  the  lines  of  force.  It  has  been  seen  that  by 
lengthening  the  plunger,  or  the  stop  of  the  stopped 
solenoid,  a  greater  pull  was  obtained,  due  to  the  greater 
superficial  area  of  the  iron.  It  is,  therefore,  evident 
that  if  the  pull  is  increased  by  this  slight  addition  in 
iron,  the  pull  should  be  very  much  increased,  for  short 
air-gaps  within  the  winding,  between  the  plunger  and 
the  stop,  if  the  return  circuit  consisted  wholly  of  iron. 

The  fact  of  placing  iron  around  the  outside  of  the 
solenoid  will  not,  however,  materially  increase  the  pull 
due  to  the  purely  solenoid  effect. 


CHAPTER   VII 


FIG.  72.  —  Iron-clad  Solenoid. 


IRON-CLAD  SOLENOID 
43.    EFFECT  OF  IRON  RETURN  CIRCUIT 

IN  practice  the  solenoid  is  usually  provided  with  an 
external  return  circuit  of  iron  or  steel,  as  in  Fig.  72. 

The  conditions  now  are  quite  different  than  in  the 
simple  solenoid.  In  this  case,  no  matter  how  much  the 

length  of  the  plunger 
may  exceed  that  of  the 
winding,  the  pull,  for 
the  same  coil  with  a 
given  magnetizing 
force,  will  be  practi- 
cally the  same  at 
points  near  the  center  of  the  winding,  whereas  in  the 
simple  solenoid  the  pull  will  vary  with  the  length  of  the 
plunger,  unless  the  coil  be  very  long,  owing  to  the  greater 
surface  of  the  protruding  plunger,  which  decreases  the 
reluctance  of  the  return  circuit  outside  of  the  winding. 
In  the  case  of  the  iron-clad  solenoid  the  lines  of  force 
are  nearly  all  concentrated  within  the  center  of  the  coil, 
and  return  through  the  iron  frame.  Hence,  no  appreci- 
able attraction  will  occur  between  the  coil  and  plunger, 
until  the  latter  is  inserted  through  the  opening  in  the 
iron  frame,  and  within  the  winding. 

Likewise,  the  pull  will  cease  when  the  end  of  the 
plunger  within  the  winding  touches,  or  protrudes  into, 
the  farther  end  of  the  iron  frame,  depending  upon 
whether  the  frame  at  this  end  is  solid  or  is  bored  through. 

102 


IRON-CLAD   SOLENOID  103 

44.    CHARACTERISTICS  OF  IRON-CLAD  SOLENOIDS 

Curve  a  in  Fig.  73  is  due  to  the  30.5-cm.  simple 
solenoid  referred  to  on  p.  95,  the  plunger  being  6.45 
sq.  cm.  in  cross-section,  as  before.  Curve  b  is  due  to  a 
test  with  the  same  coil,  but  with  an  iron  return  circuit, 
as  in  Fig.  72. 

te 


O  S  IQ  is  20  25  30 

01  STANCE    (C/KS.) 
FIG.  73.  —  Characteristics  of  Simple  and  Iron-clad  Solenoids. 

It  will  be  observed  that  the  uniform  range  is  con- 
siderably increased,  and  that  the  pull  is  very  strong  as 
the  end  of  the  plunger  within  the  winding  approaches 
the  iron  frame. 

By  boring  a  hole 
clear  through  the  rear 
end  of  the  iron  frame, 
as  in  Fig.  74,  any  jar 
due  to  sudden  stoppage 
of  the  plunger  under 
this  strong  attraction  may  be  avoided.  If  this  strong 
pull  at  the  end  of  the  stroke  is  undesirable,  only  the 
uniform  or  slightly  accelerating  portion  of  the  pull 
curve  may  be  used. 


FIG.  74.  —  Magnetic  Cushion  Type  of 
Iron-clad  Solenoid. 


104  SOLENOIDS 

45.    CALCULATION  or  PULL 

The  pull  in  kilograms  due  to  an  iron-clad  solenoid, 
at  the  center  of  the  winding,  is  calculated  by  the  same 
formula  as  for  the  simple  solenoid  ;  that  is, 

p_AOt  (IN-A\)  n,, 

981  L 

wherein  6t  =  2  -     !*         (63)    (See  p.  68.) 

1.07  Ju 

981  PL 
Hence,  'T      ~\"  (7T> 


1.01  L 

Besides  the  pull  due  to  what  may  be  termed  the  pure 
solenoid  effect,  attraction  takes  place  between  the  end 
of  the  plunger  within  the  solenoid  and  the  farther  end 
of  the  iron  frame.  This  latter  effect  may  be  approxi- 
mately expressed  by  formula  (68). 


8  TTX  981,000 

Now,  since  practically  the  entire  reluctance  of  the 
magnetic  circuit  is  in  the  air-core  or  air-gap,  the  reluc- 
tance of  the  iron  frame  may  be  neglected  in  the  design 
of  iron-clad  solenoids. 

Hence,  assuming  that  the  total  reluctance  is  in  the 
air-gap,  (45)  may  be  written 

1.  25664  IN 


I 

since  the  permeability  of  air  is  unity. 
Substituting  this  value  for  6B  in  (68), 
„_  /I.  25664  Z2V\2  A 

Jr  —  {  —     —   I    X 


(91) 


I         )      8  *x  981,000' 
whence  P  = 


IRON-CLAD  SOLENOID 


105 


The  pull  is  expressed  in  kilograms  as  before.  Pm 
represents  the  purely  magnetic  pull  between  the  plunger 
and  the  stop,  and  Ps  is  the  total  pull  due  to  an  iron- 
clad solenoid.  Hence,  Ps  —  P  +  Pm  (93),  whence 


T>    __ 


981  L 


(94) 


or 


The  iron  or  steel  frame  need  not  be  very  great  in 
cross-section,  unless  the  strong  pull  near  the  end  of  the 
stroke  is  to  be  taken  advantage  of. 

46.    EFFECTIVE  RANGE 

Figures  75  to  78  show  the  characteristics  of  several 
iron-clad  solenoids.  These  had  cast-iron  frames  and 


DISTANCE 
FIG.  75.  —  Characteristics  of  Iron-clad  Solenoid.    L  =  4.6. 


106 


SOLENOIDS 


soft-iron  plungers,  and  were  of  the  general  construction 
of  the  iron-clad  solenoid  in  Fig.  74,  with  the  brass  tube 


D/STANCE 

FIG.  76.  —  Characteristics  of  Iron-clad  Solenoid.    L  =  8.0. 


DISTANCE    (CMS') 

FIG.  77.  —  Characteristics  of  Iron-clad  Solenoid.    .£=11.4. 

in   which    the   plunger    moves    passed    clear    through 
openings   in   the   iron   frame   at   both  ends.     This  is 


IRON-CLAD   SOLENOID 


107 


known  as  the  magnetic  cmliion  type,  as  there  is  no  jar 
when  the  plunger  completes  its  stroke,  even  when  the 


DISTANCE     fc"s) 
FIG.  78.  —  Characteristics  of  Iron-clad' Solenoid.    L  =  15.2. 


125 


to  12  5 


FIG.  79.  —  Characteristics  of  Iron-clad  Solenoid.    L  =  17.8. 

attraction  is  very  great.  The  solenoid  from  which 
Fig.  79  was  obtained  had  no  hole  through  the  rear  end 
of  the  frame. 


108  SOLENOIDS 

The  general  dimensions  of  the  coils  and  plungers 
were  as  follows : 

FIG.  L  ra  A 

75  4.6  1.3  1.6 

76  8.0  1.8  3.4 

77  11.4  2.4  5.1 

78  15.2  3.1  9.6 

79  17.8  3.5  11.5 

L  and  ra  are  in  centimeters  and  A  in  square  centime- 
ters. 

From  the  foregoing,  it  may  be  generally  stated  that 
the  effective  range  of  an  iron-clad  solenoid  is  approxi- 
mately 0.6  L\  that  is,  six  tenths  of  the  length  of  the 
winding.  The  distances  in  the  charts  are  measured 
from  the  inner  attracting  face  of  the  iron  frame. 

47.    PRECAUTIONS 

The  windings  of  very  long  solenoids  should  be 
divided  into  sections;  the  reason  for  this  will  be  found 
in  Chap.  XV,  p.  201. 

The  cross-sectional  area  of  the  plunger  will  depend 
upon  the  quickness  of  action  desired.  Although  the 
action  of  a  solenoid  is  naturally  sluggish,  owing  to  the 
fact  that  the  field  due  to  the  moving  plunger  sets  up 
counter-electromotive  forces  in  the  winding,  a  fairly 
rapid  action  may  be  obtained  by  keeping  the  cross- 
sectional  area  of  the  plunger  small,  and  making  the 
ampere-turns  relatively  higher.  This  method,  however, 
is  rather  expensive,  where  the  solenoid  is  to  be  in  cir- 
cuit long. 

The  solenoid  is  unique  in  that  a  direct  pull  may  be 
obtained  over  a  long  range  of  action.  Generally  speak- 


IRON-CLAD  SOLENOID  109 

ing,  it  does  not  pay  to  use  a  lever  or  analogous  mechan- 
ism to  increase  the  range,  for  while  the  cost  of  the 
winding,  frame,  and  plunger  will  vary  directly  with  the 
length,  for  a  given  cross-section  of  winding,  frame,  and 
plunger,  it  must  be  remembered  that,  for  the  same 
amount  of  wire,  that  wound  on  a  small  radius  will  pro- 
duce more  turns  than  with  a  larger  average  radius. 
Hence,  for  the  same  amount  of  electrical  energy  more 
work  may  be  obtained,  with  the  same  amount  of 
material,  from  a  long  solenoid  than  may  be  obtained 
from  a  short  one. 

In  this  connection,  it  might  be  argued  that  it  would 
pay  to  use  a  lever  in  connection  with  a  long  solenoid, 
to  increase  the  pull,  though  reducing  the  range,  but  the 
cost  and  bother  of  the  lever  will  seldom  compensate  for 
the  advantage  gained. 


CHAPTER   VIII 

PLUNGER  ELECTROMAGNETS 

48.   PREDOMINATING  PULL 

AN  iron-clad  solenoid  provided  with  a  stop,  as  de- 
scribed at  the  end  of  Chap.  VI,  p.  99,  is  known  as  a 
Plunger  Electromagnet. 
(See  Fig.  80.) 

While  in  the  simple 
and  iron-clad  solenoids 
the  predominating  pull 
is  between  the  magne- 
tizing force  due  to  the          FlG-  80.  — Plunger  Electromagnet. 
current  in  the  winding  and  the  flux  in  the  iron  plunger, 
the  pull  due  to  the  flux  in  the  plunger  and  stop  pre- 
dominates in  the  plunger  electromagnet. 


49.    CHARACTERISTICS 

The  curves  a  and  b  in  Fig.  81  are  the  same  as  in 
Fig.  73  and  are  due  to  the  iron-clad  solenoid  in  Fig.  72 
with  the  30.5-cm.  coil.  Curve  c  was  obtained  with  a 
stop  25  per  cent  of  the  length  of  the  winding,  while 
the  stop  used  in  obtaining  curve  d  was  twice  as  long ; 
that  is,  50  per  cent  of  the  winding  length.  The 
plunger  was  6.45  sq.  cm.  in  cross-section. 

These  characteristics  are  particularly  interesting  as 
they  are  obtained  from  an  actual  test  *  made  by  the 


*  Electrical  World  and  Engineer,  Vol.  XLV,  1905,  pp.  934-935. 

110 


PLUNGER  ELECTROMAGNETS 


111 


author.  The  magnet  had  a  massive  wrought-iron  re- 
turn circuit.  The  curves  e  and  /  are  calculated  by 
formula  (92). 

P    - 
m 


IN 


3951  1 


POSITION     IN  COIL     (CMS) 
FIG.  81.  —  Characteristics  of  Plunger  Electromagnet. 

Inspection  of  these  curves  will  show  that  if  the  heights 
of  curve  e  be  added  to  those  of  curve  5,  curve  g  will  be 
the  result.  Likewise,  the  addition  of  the  heights  of 
curves/"  and  b  will  produce  curve  h. 

50.    CALCULATION  OF  PULL 
Now,  curves  g  and  h  are  calculated  by  formula  (95). 

pmiA  \et(iN-A^>    (  jarvn 

L       981 L  V3951 1)  J 

The  reason  why  the  actual  and  calculated  values  do 
not  coincide  is  on  account  of  the  magnetic  reluctance 
of  the  iron  plunger  at  so  high  a  density.  All  the 
curves  in  Fig.  81  are  due  to  10,000  ampere-turns. 


112  SOLENOIDS 

By  assuming  the  reluctance  to  be  equivalent  to  one 
centimeter  length  of  air-gap,  under  these  conditions, 
curves  g  and  Ti  will  exactly  coincide  with  curves  o  and 
d,  respectively. 

Part  of  the  quantity  assigned  to  reluctance  is  due  to 
leakage,  but  it  is  easier  to  consider  it  all  as  reluctance, 
if  provisions  are  made  for  it.  (See  p.  39.) 

51.    EFFECT  OF  IRON  FRAME 

Excepting  for  a  very  short  range  of  action,  the 
reluctance  of  the  iron  frame  appears  to  have  but 
little  effect  at  this  high  density  in  the  plunger  and 
stop. 

The  curve  marked  %  in  Fig.  81  is  due  to  using  the 
same  coil,  plunger,  and  stop,  as  in  the  test  which  gave 
curve  c,  but  with  no  iron  return  circuit.  A  large 
block  of  iron  was,  however,  placed  at  the  rear  end  of 
the  coil. 

It  will  be  noticed  that  the  lower  part  of  the  curve  i 
tends  to  follow  the  lower  part  of  curve  a,  which  would 
seem  perfectly  natural,  as  there  was  no  iron  at  the 
mouth  of  the  winding  other  than  the  plunger  itself, 
when  curves  a  and  i  were  made. 

This  would  indicate  that  it  is  not  necessary  to  use  a 
very  heavy  iron  frame,  and  that  the  magnetic  connec- 
tion between  the  plunger  and  the  frame  at  the  mouth 
of  the  winding,  is  not  a  matter  of  much  importance  for 
a  high  m.  m.  f. 

In  the  foregoing,  the  flux  density  was  very  high  for 
short  air-gaps.  It  is  evident,  however,  that  for  a  short 
range  of  action,  it  is  more  important  to  work  with  low- 
flux  densities.  Hence,  for  short  air-gaps  and  with 


PLUNGER   ELECTROMAGNETS  113 

about    75  per  cent  saturation,  formula    (95)    may  be 
reduced  to 


In  this,  the  value  of  6t  is  made  maximum,  i.e.  2,  and 
X  reduced  to  zero.  As  the  reluctance  of  the  air-gap 
will  be  practically  all  the  reluctance  in  the  circuit,  only 
a  slight  allowance  may  be  made  for  leakage. 

While  no  exact  rule  for  the  reluctance  (including 
leakage,  and  the  bulging  of  the  lines  around  the  air- 
gap)  may  be  set  forth,  unless  an  exact  knowledge  of 
the  iron  characteristics  are  known,  the  statement  re- 
garding allowances  for  solenoids,  given  in  Art.  37, 
p.  80,  will  hold  for  plunger  electromagnets  also. 

52.   MOST  ECONOMICAL  CONDITIONS 

The  proper  flux  density  may  be  determined  by 
a  method  due  to  Mr.  E.  R.  Carichoff.  To  quote 
from  one  of  his  articles*  "  The  main  facts  that  seemed 
to  the  writer  as  useful  are  that  there  is  a  certain  length 
of  air-gap  for  any  given  magnet  of  uniform  cross- 
section  where  the  pull  between  armature  ajid  poles  is 
lessened  if  the  polar  area  is  either  increased  or  dimin- 
ished, and  that  the  pull  under  these  conditions,  multi- 
plied by  the  length  of  the  air-gap,  is  greater  than  the 
pull  with  any  other  air-gap  multiplied  by  the  length 
of  the  latter." 

The  following  explanation  of  his  method  f  is  here- 
with reproduced  : 

*  The  Electrical  World,  Vol.  XXIII,  1894,  pp.  113-114. 
t  The  Electrical  World,  Vol.  XXIII,  1894,  pp.  212-214. 


114 


SOLENOIDS 


Let  us  assume,  for  example,  that  the  curve  in  Fig.  82, 
OECD,    represents    the     iron,    and     OF   the    air-gap 

is  (ton , , , , . 


13,000 


2,000 


FIG.  82.  —  Method  of  determining  Proper  Flux  Density. 

characteristic,  and  that  we  are  working  at  the  point  0 
on  said  curve.  Reduce  the  polar  area  by  dA,  and 
suppose  that  the  force  is  reduced  for  an  instant  by  dF, 
so  that  the  induction  in  the  air-gap  is  still  SB  and  that 
in  the  iron  is  reduced  by  A6&  Since  a  tangent  drawn 
to  the  curve  at  0  is  parallel  to  the  line  OF,  we  see  that 
the  force  necessary  to  produce  a  change  A£B  in  the  in- 
duction is  the  same  in  both  iron  and  air-gap.  There- 
fore, if  (^produces,  in  iron,  a  change  A6B,  it  can  produce 
JA68,  say  d68,  in  both. 

It  is  evident  that  with  the  above  assumptions 


PLUNGER  ELECTROMAGNETS  115 

With  area  A  and  induction  66  the  pull  is  proportional 


to 

With  the  area  (A  —  dA)  and  the  induction  66+ 
we  have  (66  +  dcj6)2(A  —  dA)  proportional  to  pull. 

Then         £ffA  <  =  >  (t£+d£&)\A  -  dA),          (97) 


if  c'C       <=><&& 

1  dA 

Since  for  this  case  c?66  =  -66—  7-,  the  two  sides  of  the 

2  ^L 

equation  are  the  same  and  the  pull  is  the  same  when 
the  polar  area  is  A,  and  when  it  is  A  —  dA.  In  the 
same  way  it  can  be  shown  that  the  pull  is  the  same 
where  the  polar  area  is  A  and  A  4-  dA. 

From  this  we  draw  the  conclusion  that  when  the  air- 
gap  reluctance  is  expressed  by  a  line  parallel  to  the 
tangent  drawn  at  the  part  of  the  iron  characteristic 
where  we  are  working,  there  is  no  gain  by  either 
increasing  or  decreasing  the  polar  area.  This  is  evi- 
dently the  condition  of  maximum  efficiency,  as  we 
shall  see  from  further  considerations. 

Keep  the  same  characteristics  and  suppose  our 
ampere-turns  put  us  at  the  point  D  on  the  iron  curve. 
Decrease  the  polar  area  by  dA,  and  for  an  instant  the 
force  by  dO--,  so  that  66  is  still  the  induction  in  the  air- 
gap.  d&  is  now  much  greater  than  before  necessary  to 
make  the  change  A66,  so  that  it  will  produce  a  change 
in  the  whole  circuit  by  an  amount  dOo  referred  to  air- 
gap,  where  d£Q  is  greater  than  JA66,  or  greater  than 

1     dA 

-66-:-  •  This  condition  makes  the  right-hand  member 
Z  A. 

of  equation  (97)  greater  than  the  left-hand  member, 
showing  that  the  pull  is  increased  by  decreasing  the 


116 


SOLENOIDS 


polar  area.  Increase  the  polar  area  by  dA,  keeping 
other  conditions  as  above,  and  equation  (97)  shows 
that  the  pull  is  decreased.  Therefore,  if  our  iron 

curve    shows   that  — ^  is  greater  than  the  same  func- 

dtf 

tion  for  the  air-gap,  the  air-gap  reluctance  should  be 
increased  until  the  two  functions  are  the  same. 

Again,  at  the  point  E  we  find  that  d£f  is  less  than  in 
the  case  first  cited,  and  if  the  same  reasoning  is  followed, 
it  is  found  that  the  pull  is  increased  by  increasing  the 
polar  area. 

Instead  of  increasing  or  decreasing  the   polar  area, 


1 

—  - 

;s-- 

•PH 

.1    - 

^ 

1^ 

vT 

—  — 

—  - 

—  — 

-^ 

*<*- 

.—  - 

^s- 

•*ct 

^T 

——  • 

•   •• 

-»— 

• 

.Hi 

X" 

^_ 

^^+ 

^ 

^T 

»*-? 

^0 

,—  - 

—  — 

•     " 

•1     1— 

•.  • 

V 

s 

2 

X** 

"^ 

a 

CO 

i-M-hh 

^x 

x* 

$<4¥ 

f 

Si      1  // 

'Tf: 

2,000  j*— 

LL 

0 

5            ifr          1ft           80          26           30          35           40          45           60           a 

FIG.  83.  —  c^<S3  Curves  for  Iron  and  Air-gap. 

the  same  results  are  obtained  by  shortening  or  length- 
ening the  air-gap.     When   this  is   done,  so   that   the 


PLUNGER  ELECTROMAGNETS  117 

function  —  —  is    the    same  for  iron   and    air-gap,  the 

pull  multiplied  by  the  distance  is  a  maximum.  This 
being  the  case,  the  best  results  are  obtained  by  using 
the  proper  air-gap  ;  and  if  this  distance  is  not  the 
travel  required,  a  lever  can  be  used  to  multiply  or 
divide  with. 

With  these  principles  in  view,  it  is  easy  to  get  the 
most  efficient  possible  arrangement.  It  is  also  easy  to 
predetermine  a  magnet  to  pull  required  amounts  in 
more  than  one  point  of  its  travel. 

By  drawing  tangents  to  all  points  of  the  iron  curve 
and  lines  from  the  origin  parallel  to  those  tangents, 
and  intersecting  these  by  horizontal  lines,  we  get  the 
curve  of  proper  air-gap  for  all  points  of  iron  curve  cut 
by  said  horizontal  lines.  (See  Fig.  .83.) 

To  prove  that  the  air-gap  thus  determined  gives  the 
maximum  amount  of  work,  where  work  equals  initial 
pull  times  length  of  air-gap,  change  I  by  dl  ;  then 


60        l 
We  see  that  for  the  point  F 


3     A68 

and  d£B 

and  for  points  to  the  right  of  F, 


and  for  points  to  the  left  of  F, 


118 


SOLENOIDS 


In  the  three  cases  the  work  will  be  proportional  re- 
spectively to  cgpi  .,. 

(2) 

(3) 


In  Fig.  84  is  shown  the  result  of  a  test  made  by  the 
author  with  the  i=17.8,  ra=3.5,  -4  =  11.5,  solenoid,  sur- 


12 


H 


1& 


X8         70 


KILO    IN 
FIG.  84.  —  Air-gaps  for  Maximum  Efficiency. 

rounded  by  a  cast-iron  frame.  The  stop  extended  through- 
out nearly  one  half  the  length  of  the  winding,  which  is 
the  position  of  maximum  pull,  as  will  be  shown  presently. 


PLUNGER  ELECTROMAGNETS 


119 


Reference  to  this  diagram  will  show  that  the  most 
economical  condition,  with  this  particular  plunger  elec- 
tromagnet, is  met  with  a  1.27-cm.  air-gap,  for  25 
cm. -kg.  of  work,  while  for  50  cm. -kg.  the  length  of 
the  air-gap  would  be  slightly  greater.  This  shows 
plainly  that  only  the  best  grades  of  iron  or  steel  should 
be  used  where  high  efficiency  is  desired. 

53.    POSITION  OF  MAXIMUM  PULL 

Figure  85  is  the  result  of  a  test  of  the  above  magnet, 
with  a  constant  air-gap  of  1.27  cm.  and  various 
lengths  of  stops.  The  position  of  gap  is  measured 
from  the  inner  end  of  the  frame. 


II 

1  =  10,1 

OO 

50 

^ 

-^ 

^ 

\ 

x 

~? 

^- 

— 

~^- 

-^ 

x 

/ 

^s- 

^ 

IN-  1 

3,000 

X 

^ 

^ 

^ 

,--- 

^~^ 

^^ 

\ 

^ 

-""' 

0            >           2           3          <7           5          6           7         2 

?          9          /O         //         /<! 

POS/7/0/V    OF  GAP 
FIG.  85.  — Test  showing  Position  of  Air-gap  for  Maximum  Pull. 

It  is  self-evident  that  the  maximum  pull  is  obtained 
when  the  center  of  the  air-gap  is  at  the  center  of  the 
winding,  assuming  the  winding  to  be  equally  distrib- 
uted between  the  limits  of  the  iron  frame. 


120 


SOLENOIDS 
54.    CONED  PLUNGERS 


It  has  been  shown  that  there  is  a  certain  relation 
between  polar  area  and  length  of  air-gap  which  will 
produce  the  most  economical  conditions  ;  hence,  if  the 
length  of  the  air-gap  is  to  be  increased,  the  polar  area 
must  be  increased  also.  However,  if  the  diameter  of 
the  plunger  be  increased,  there  may  not  be  enough 
room  for  the  winding  if  the  space  is  limited. 


^ 


BRASS  RING 


•/O  CMS. 


CMS 


PIN 


FIG.  86.  —  Flat-faced  Plunger  aiid  Stop. 

From  another  article  by  Mr.  E.  R.  Carichoff,*  part 
of  the  following  is  taken  : 

Figure  86  shows  the  dimensions  of  a  cast-steel  electro- 
magnet, which,  with  an  air-gap  of  0.316  cm.,  pulls  545 
kg.  when  the  exciting  power  is  4800  ampere-turns  in 


*  The  Electrical  World,  Vol.  XXIV,  1894,  p.  122. 


PLUNGER  ELECTROMAGNETS 


121 


either  shunt  or  series  coil.  This  gap  is,  for  this  par- 
ticular case,  the  one  which,  multiplied  by  the  pull  of 
545  kg.,  gives  a  maximum,  or  173  cm. -kg.  In  case 
a  movement  over  1.27  cm.  instead  of  0.816  cm.  is  re- 
quired, the  plunger  of  the  magnet  may  be  attached  to 
the  short  end  of  a  4  to  1  lever,  at  the  long  end  of  which 
the  travel  will  be  1.27  cm.,  and  the  pull  136  kg.,  or,  as 
before,  173  cm. -kg.  If,  however,  the  plungers  are  sim- 
ply separated  1.27  cm.,  the  initial  pull  becomes  about 
60  kg.,  which,  multiplied  by  1.27  cm.,  gives  76  cm. -kg., 
or  less  than  one  half  of  what  can  be  obtained  by  using 
the  lever. 

In  this  it  is  assumed  that  the  force  to  overcome  is 
fairly  constant,  or  but  slightly  increasing.  Of  course, 
if  the  force  to  be  over- 
come varies  directly 
with  the  pull  of  the 
magnet,  there  is  no 
need  to  bother  about 
the  air-gap. 

It  is  possible  to  get 
a  direct  pull  of  136  kg. 
at  a  distance  of  1.27 
cm.  by  using  the  form 
of  magnet  in  Fig.  87, 
which  was  suggested 
and  adapted  by  Lieu- 
tenant F.  J.  Sprague. 
The  only  change  is  in 
the  air-gap.  With  the 
angles  there  shown  for 

,,  ,  i     p          i  FIG.  87.  —  Coiied  Plunger  aiid  Stop. 

the   male   and  female 

cone  plungers  it  is  readily  seen  that  the  area  of  air-gap 


122 


SOLENOIDS 


is  approximately  doubled,  and  its  length  also  doubled, 
while  the  reluctance  is  approximately  the  same  as  that 
of  the  arrangement  in  Fig.  86. 

It  is  further  readily  seen  that  the  travel  of  plunger 
is  1.27  cm.  instead  of  0.316  cm.,  as  in  Fig.  86. 

As  the  reluctance  of  the  circuit  is  approximately  the 
same  as  in  Fig.  86,  the  total  number  of  magnetic  lines 
is  approximately  the  same,  but  as  these  lines  are  dis- 
tributed over  an  air-gap  of  double  the  area,  and  the 
force  makes  an  angle  of  60  degrees  with  the  direction 
of  travel,  the  pull  is  only  136  kg.  at  1.27  cm.  This 

pull  of  136  kg.  times  1.27 
cm.  is,  however,  173  cm.  -kg., 
as  before. 

To  change  polar  area 
and  travel,  keeping  the 
reluctance  approximately 
constant:  Assume  the  ap- 
proaching poles  to  be  two 
cylinders  with  male  and 
female  conical  extremities, 
as  in  Fig.  88. 


/  a\  _\    and  d  the  travel,  and  I  the 

proper  length  of  air-gap  for 
a  right  section,  A1  is  the 
polar  area,  V  is  the  air-gap 
length,  and  d'  the  travel 


FIG.  88.  -Comparison  of  Dimen- 

sions  and    Travel    of    Flat-fat-ed 
and  Coned  Plungers  and  Stops. 


when  the  anofle  at  the  base 


Qf 


CO116  becomes  a. 


Condition  of  constant  reluctance  is  —  =  —  • 

A'     A 


PLUNGER   ELECTROMAGNETS  123 

But  A  =  A'  cos  a  and  I'  =  d'  cos  «. 

d'  cos  a  d 


Therefore, 


A.'  cos  a 


whence  cos2 a  =  — -  and  =  — 

d'          A'2      d' 

Thus,  if  the  polar  area  is  doubled  in  this  way,  the 
travel  is  increased  four  times. 

It  is  also  seen  that  V  differs  more  or  less  from  the 
true  length  of  air-gap  according  to  position  of  conical 
surfaces. 


FIG.  89. —  Flux  Paths  between  Coned  Plunger  and  Stop. 

Figure  89  shows  the  flux  paths  for  a  V-shaped  air-gap 
between  two  pieces  of  iron,  which  may  be  considered 
as  a  good  representation  of  the  conditions  in  the  air- 
gap  of  the  plunger  electromagnet  in  the  article  above 
quoted. 

The  effect  of  changing  the  angles  of  pointed  plungers 
is  shown  in  Fig.  90,  which  curves  are  due  to  the  L  —  17.8, 
ra  =  3.5,  A  =  11.5,  plunger  electromagnet  previously 
referred  to.  The  stop  extended  35  per  cent  through 


124 


SOLENOIDS 


the  coil.     These  effects  are  due  to  20,000  ampere-turns. 
In  practice,  a  larger  plunger  and  lower  m.  m.  f.  should 
be  employed. 
/6 


LEN&TH    OF  AIR- GAP 

FIG.  90.  —  Effect  of  chauging  Augles. 

Mr.  W.  E.  Goldsborough  *  has  described  the  electro- 
magnet shown  in  Fig.  91,  which  is,  no  doubt,  the  best 

*  Electrical  World  and  Engineer,  Vol.  XXXVI,  1900. 


PLUNGER  ELECTROMAGNETS 


125 


application  of  the  coned  plunger,  as  the  conical  portion 
of  the  plunger  is  the  same  length  as  the  winding.     In 


Density  In  air  gap=-  0500  gausses. 
3820  turns  of  *18  fl.  W.G.,  D  C.C. 
2.01  amperes  required  at  55  volts 
Working  temperature  =43.0°c. 
Use  cast  steel  in  magnetic  circuit- 
Weight  wire  on  magnet,  ^  35  Ib. 


FIG.  91.  —  Design  of  a  Tractive  Electromagnet  to  perform  400  cm  .-kg. 

of  Work. 

this  case  the  range  is  so  short,  and  the  attracting  area 
so  great,  that  the  solenoid  effect  may  be  entirely  neg- 
lected, and  formula  (68)  may  be  employed.  (See 
p.  76.) 

55.   TEST  OF  A  VALVE  MAGNET 

The  following  test,*  described  by  Mr.  C.  P.  Nachod, 
is  of  interest. 

This  magnet,  shown  in  Fig.  92,  has  a  short  stroke, 
and  is  designed  to  operate  an  air-valve  by  means  of  a 

*  Electrical  World  and  Engineer,  Vol.  XL VI,  1905,  p.  1071. 


126 


SOLENOIDS 


brass  rod  (not  shown)  passing  through  the  hole  in  the 
core.  The  core  and  armature  are  of  Norway  iron;  the 
core  has  an  outside  diameter  of  3.17  cm.  and  has  a 
0.95-cm.  hole  through  it.  The  magnet  is  of  the  iron- 
clad type  with  cast-iron  shell  and  top.  There  is  a 
cylindrical  clearance  gap  between  the  armature  and 
top,  which,  being  invariable,  has  not  been  considered. 

There  are  two  exciting 
coils,  A  and  B .  The  for- 
mer, having  1860  turns  of 
No.  25  wire,  is  used  as  an 
operating  coil  to  draw 
down  the  armature ;  and 
the  latter,  of  1765  turns 
of  No.  26  wire,  serves  as  a 
retaining  coil  to  hold  it 
down  against  the  air-pres- 
sure, after  the  circuit  in 
the  other  coil  is  broken. 
Coil  A,  as  shown  in  Fig. 
92,  is  located  so  as  to  en- 


FIG.  92.  —  Valve  Magnet. 

circle  the  working  air-gap,  which  is  not  the  case 
with  B. 

The  test  was  made  with  a  simple  traction  permeame- 
ter,  definite  air-gaps  being  obtained  by  measured  brass 
washers. 

Figure  93  shows  the  pull  produced  with  varying  exci- 
tation for  each  coil  separately,  with  a  constant  air-gap 
of  0.41  mm.  In  the  curve  for  coil  A  the  range  of 
magnetic  densities  is  sufficient  to  show  clearly  the 
change  in  permeability  of  the  iron  circuit.  For  so 
small  an  air-gap  the  difference  between  the  pulls 
produced  by  the  two  coils  with  the  same  magnetizing 


PLUNGER   ELECTROMAGNETS 


127 


force  is  remarkably  great.     The  ratio  of  these  pulls 
lias  been  plotted,  and  the  curve  shows  that  coil  B  is 


AMPERE-TURA/S 

FIG.  93.  —  Characteristics  of  Valve  Magnet. 

only  from  0.4  to  0.8  as  effective  as  A,  due  solely  to 
its  position  on  the  core,  which  permits  a  larger  mag- 
netic leakage. 

Figure  94  shows  the  same  relations  with  an  air-gap  of 
2.05  mm.  or  five  times  as  great  as  in  the  previous  case. 
With  this  gap  the  range  of  flux  density  is  not  great 
enough  to  produce  an  inflection  point  in  either  curve  ; 
and  the  ratio  of  pulls  for  the  same  excitation  is  more 


128 


SOLENOIDS 


nearly  constant,  averaging  a  little  over  0.7,  but  decreas- 
ing with  decreasing  density. 

From  the  curves  it  appears  that  if  it  were  desired  to 
connect  the  coils  in  series  so  that  the  magnetic  effect 


l.o 


0.8 


0.6 


FIG.  94. — Characteristics  of  Valve  Magnet. 


of  B  would  neutralize  that  of  A,  it  would  be  possible 
to  do  so  for  only  one,  instead  of  all  current  values,  and 
that  such  a  neutralizing  coil  for  all  current  values 
should  have  the  same  axial  length  and  slide  within 
or  without  the  other. 


PLUNGER  ELECTROMAGNETS 


129 


56.    COMMON  TYPES  OF  PLUNGER  ELECTROMAGNETS 

The  general  design  of  the  frames  of  plunger  electro- 
magnets is  optional,  providing  the  flux  passes  from  the 
frame  to  the  plunger 
uniformly  on  all 
sides,  so  as  not  to 
attract  the  latter 
sidewise. 

The  plunger 
usually  travels 
within  a  brass  tube 
placed  within  the 
insulated  winding. 


FIG.  95.  —  Horizontal  Type  Plunger  Electro- 
magnet. 


Any  form  of  guide  consisting  of 


FIG.    96.  —  Horizontal   Type    Plunger 
Electromagnet. 

non-magnetic  material  may  be 
employed. 

In  Figs.  95 
to  97  there  are 
shown  several 
common  types. 

The      magnet    FIG.  97.  —  Vertical  Type  Plunger 
in  Fig.  98  has  Electromagnet. 

no  outer  frame  ;  nevertheless,  it  has  a 
closed  magnetic  circuit  outside  of  the 

FIG.      98.  —  Two-coil 
Plunger  Electromag-  Working  air-gap, 
net. 


130 


SOLENOIDS 


FIG.  99.  — Pushing  Plunger 
Electromagnet. 


57.    PUSHING  PLUNGER  ELEC- 
TROMAGNET 

Where  a  pushing  effect  is 
desired,  the  plunger  electro- 
magnet may  be  inverted,  and 
a  brass  rod  fastened  to  the 
plunger  and  passed  through 
the  stop,  as  in  Fig.  86,  Art.  54. 
A  magnet  of  this  type  is 
shown  in  Fig.  99  attached  to  a 
whistle  valve. 


58.    COLLAR  ON  PLUNGER 

By  placing  a  collar  on  the  plunger  outside  of  the 
frame,  as  in  Fig.  100,  the  pull  may  be  considerably 
increased. 


FIG.  100.  —  Electromagnet  with  Collar  on 
Plunger. 

This  is  due  to  the  flux  which  passes  from  the  frame 
to  the  plunger,  at  the  opening  through  the  frame. 


CHAPTER   IX 


ELECTROMAGNETS   WITH  EXTERNAL  ARMATURES 

59.    EFFECT  OF  PLACING  ARMATURE  OUTSIDE  OF 
WINDING 

IN  Fig.  100*  is  shown  the  effect  of  ascertaining  the 
pull  due  to  the  magnet  in  Fig.  102  (also  referred  to  in 

12 


/O 


3- 


POSITION  OF  GAP    CCMS.) 

FIG.  101.  — Characteristics  of  Test  Magnet. 

*  American  Electrician,  Vol.  XVII,  1905,  pp.  299-302. 
131 


132 


SOLENOIDS 


Art.  42),  by  using  two  cores  of  the  same  length,  sepa- 
rated by  a  brass  disk  0.89  mm.  thick,  which  represented 
the  air-gap  (the  permeability  of  brass  being  the  same  as 
for  air).  The  ampere-turns  were  6300. 

It  will  be  observed  that  when  the  abutting  ends  of 
the  cores  were  at  the  end  of  the  winding,  the  pull  was 
only  approximately  one  half  of  what  it  was  at  the  center 
of  the  coil. 


FIG.  102.  — Test  Magnet. 

This  effect  is  easily  explained.  When  the  abutting 
ends  are  at  the  mouth  of  the  winding,  the  leakage  is  so 
great  that  only  about  seven  tenths  of  the  total  flux 
passes  through  the  working  air-gap. 

60.    BAR  ELECTROMAGNET 

When  the  core  and  coil  are  in  the  relative  positions 

as  shown  in  Fig.  103,  they 
constitute  the  Bar  Elec- 
tromagnet. Its  field  is  very 
similar  to  that  of  the  bar 
permanent  magnet. 

To  obtain  good  results 


FIG.  103.  —  Bar  Electromagnet. 

from  this  type  the  ends  of  the  core  should 

be  bent  as  in  Fig.  104 ;  but  if  these  limbs 

be  very  long,  the  leakage  between  them 

will  be  great.     A  similar  effect  may  be  FiG^04^Eiec- 

obtained  by  bending  the  armature  instead      tromagnet  with 

P  ,,  Winding         on 

of  the  core.  Yoke.  ' 


ELECTROMAGNETS   WITH   ARMATURES         133 


61.   RING  ELECTROMAGNET 

The  effect  of  bending  a  bar  electromagnet  into  a  circle 
is  shown  in  Fig.  23,  p.  37.  This  is  called  a  Ring  Electro- 
magnet. This  type  has  the  minimum  leakage,  but  if  the 
radius  of  the  ring  be  small,  the  turns  constituting  the 
exciting  coil  tend  to  crowd  at  the  inside  of  the  ring,  which 
increases  the  total  length  of  wire  and  reduces  the  ampere- 
turns  for  a  given  voltage ;  while  if  the  radius  be  large,  the 
reluctance  of  the  magnetic  circuit  will  be  correspondingly 
great. 

62.    HORSESHOE  ELECTROMAGNET 

The  natural  method,  then,  is  to  bend  the  core  in  the 
form  of  U  and  place  a  coil 
on  each  limb  as  in  Fig.  105. 
This  form  is,  however,  rather 
inconvenient  to  make,  and 
the  bend  takes  up  too  much 
room,  as  a  rule;  therefore, 
the  practical  horseshoe  elec- 


FIG.  106.  —  Practical  Horseshoe 
Electromagnet. 


FIG.  105.  —  Horseshoe  Electro- 
magiiet. 

tromagnet  is  made  of  three 
pieces,  besides  the  armature. 
In  this  form,  Fig.  106,  the 
wire  is  wound  directly  on  to 
the  insulated  cores,  and  the 
latter  are  then  fastened  to 


the  yoke,  or  "back  iron,"  as  it  is  often  called. 


134 


SOLENOIDS 


In  Fig.  107  is  shown  a  modification  of  the  horseshoe 
electromagnet.  This  is  also  comparable  with  the  bar 
electromagnet  with  one  of  its  core  ends  bent  around  near 

•     the  opposite  end  of  the  core. 
This  is  not  so  economical  as  the  two- 
jj   coil  electromagnet,  as  there  cannot  be  so 

many  ampere-turns  for  the  same  amount 

FIG.  107. -Modified  J         ^ 

Form  of  Horseshoe   O*  copper  ior  one  coil  ot  large  diameter 

Electromagnet.        as  witn  two  coils  of  smaller  diameter,  for 

the  same  total  current,  as  is  pointed  out  in  Art.  164,  p.  284. 

63.    TEST  OF  HORSESHOE  ELECTROMAGNET 

The  result  of  a  test  of  the  magnet  in  Fig.  108  is 
shown  in  Figs.  109  and  110. 

SO. 48  CMS 

~T 


1 

j  ,  —  1  

1              I.' 
II            1, 

: 

J       ! 

to 


1  i 


I 


[f  141  C/MS»| 


CMS. 


u. 


•3-5    CMSr 
FIG.  108.  —  Experimental  Electromagnet. 

It  will  be  observed  that  the  pull  is  strong  for  very 
short  air-gaps,  but  weak  when  the  armature  is  removed 
a  short  distance  from  the  cores. 


ELECTROMAGNETS   WITH  ARMATURES        135 


LENGTH  OF  GAP  (CMS.) 
FIG.  109.  —  Characteristics  of  Horseshoe  Electromagnet. 


KILO    IN 

FIG.  110.  — Relation  of  Work  to  Length  of  Air-gap. 


136 


SOLENOIDS 


Since,  in  this  case,  there  are  two  air-gaps,  the  total 
air-gap  is  twice  that  indicated  in  Figs.  109  and  110. 

The  dotted  curve  in  Fig.  110  represents  0.2  cm. -kg. 
of  work.  It  will  be  observed  that  the  most  economical 
condition  for  this  amount  of  work  is  met  with  0.1-cm. 
(1  mm.)  air-gap. 


FIG.  111.  — Iron-clad  Electro- 
magnet. 


64.    IRON-CLAD  ELECTROMAGNET 

This  type  maybe  divided  into  two  classes,  one  of  which 
is  usually  of  small  dimensions  and  consists  of  a  piece  of 

soft-iron  tubing  with  a  soft- 
iron  disk  at  one  end  to  which 
the  core  of  the  spool  contain- 
ing the  winding  is  fastened, 
Fig.  Ill,  or  else  it  is  made 
from  a  solid  piece  of  iron,  or 
steel  casting,  by  turning  a 
groove  to  receive  the  excit- 
ing coil.  The  latter  construc- 
tion is  usually  adhered  to  in  large  magnets. 

Small  iron-clad  electromagnets  are  used  extensively  in 
telephone  switchboard  apparatus  where  the  range  of 
action  is  not  great  and  the  duration  of  excitation  is 
brief.  The  fact  that  it  is  not  materially  affected  by 
external  magnetic  influence  makes  it  particularly 
adapted  for  this  purpose. 

Its  use  is  limited  to  cases  where  the  range  or  attract- 
ing distance  is  small,  owing  to  the  great  leakage 
between  the  core  and  outer  shell  when  the  armature  is 
removed  for  even  a  small  distance. 

The  iron-clad  electromagnet  is  also  employed  where 
a  very  strong  attraction  is  desired  when  the  armature 


ELECTROMAGNETS   WITH   ARMATURES         137 

is  in  actual  contact  with  the  polar  surfaces.  Since  in 
this  case  the  air-gap  is  exceedingly  small,  so  many 
ampere-turns  are  not  required,  and  the  magnetic  circuit 
may  be  made  very  short. 

Electromagnets  of  this  class  are  fitted  with  tool-hold- 
ing devices  and  may  be  rigidly  held  to  the  beds  or  frames 
of  machines  in  any  desired  position  by  simply  turning 
on  the  current.  They  are  also  employed  for  gripping 
iron  pipe,  pig,  etc.,  while  the  latter  are  being  hoisted. 

65.    LIFTING  MAGNETS 

Electromagnets  of  the  iron-clad  type  have,  in  recent 
years,  come  into  general  use  in  large  industrial  plants 
for  handling  iron  and  steel  of  every  description,  both 
hot  and  cold. 

Some  of  the  principal  types  are  shown  in  the  follow- 
ing illustrations.* 

Figure  112  shows  a  "  skull-cracker  "  at  work  reducing 
a  scrap  heap.  The  large  steel  ball  is  gripped  by  the 
magnet,  both  lifted  by  the  crane,  the  current  turned  off, 
and  the  ball  drops,  reducing  the  large  pieces  of  scrap  to 
small  pieces  which  may  be  easily  handled.  The  same 
magnet  is  employed  to  place  the  large  pieces  in  position 
and  to  remove  the  broken  pieces.  These  latter  opera- 
tions are  similar  to  that  shown  in  Fig.  113,  wherein 
scrap  is  being  unloaded  from  cars  by  means  of  the 
magnet. 

Another  type,  known  as  Plate  and  Billet  Magnet,  is 
shown  in  Fig.  114. 

In  Fig.  115  is  shown  an  Ingot  Magnet  lifting  an  ingot 
mold.  There  are  many  other  uses  for  these  magnets. 

*  Electric  Controller  and  Supply  Co. 


138 


SOLENOIDS 


ELECTROMAGNETS   WITH   ARMATURES         139 


140 


SOLENOIDS 


FIG.  114.  —  Plate  and  Billet  Magnet. 


ELECTROMAGNETS   WITH   ARMATURES         141 


FIG.  115.  —  Ingot  Magnet. 


142  SOLENOIDS 

The  cost  of  handling  the  melting  stock  used  -by  open- 
hearth  furnaces  from  cars  to  stock  pile,  or  from  stock 
pile  to  charging  boxes,  has  been  reduced  from  approxi- 
mately eight  cents  a  ton  by  hand  methods  to  two  cents 
a  ton  by  the  use  of  magnets  in  connection  with  suitable 
cranes. 

66.    CALCULATION  OF  ATTRACTION 

The  relation  between  ampere-turns  and  pull,  for  the 
air-gap  alone,  is 


wherein  P  is  the  pull  in  kilograms,  Ag  the  cross-sectional 
area  of  each  gap  (if  more  than  one),  and  lg  the  length  of 
the  air-gap  in  centimeters. 
Transposing, 

Zy-8051*,*/^.  (99) 

Aa 

For  electromagnets  of  the  type  shown  in  Fig.   107 
the  complete  formula  (including  leakage,  see  p.  39)  is 


(100) 
while  for  the  horseshoe  type 

(101) 


wherein  lc  =  length  of  each  core  or  limb  in  centimeters 
and  cfhi  is  the  reluctance  between  parallel  cores,  limbs, 
or  surfaces  per  centimeter  length. 

These    formulae   are,   however,    only    approximately 
correct. 


ELECTROMAGNETS  WITH   ARMATURES        143 


Where  the  end  area  of  the  core  is  not  the  same  as 
the  attracting  surface  of  the  armature,  Ag  will  be  the 
average  between  the  two  areas. 

An  electromagnet  designed  to  attract  its  armature 
through  a  given  distance  may  be  made  more  effective 

by  increasing  the  attracting  areas       j 1 

of  either  the  core  or  armature  or 
both.  This  may  preferably  be 
accomplished,  as  in  Fig.  116. 

The  lifting  power  of  electro- 
magnets of  the  class  described  in 
Art.  65  may  only  be  determined 
by  experience,  since  it  is  impos- 
sible to  predetermine  the  attract-  I  I 
ing  areas  and  air-gaps  of  the  scrap  FlG-  m*.  — Method  of  iu- 

-.      ,.,.,     ,  creasing  Attracting  Area. 

to  be  lifted. 

There  is  a  peculiar  phenomenon  in  connection  with 
these  magnets.  Before  the  material,  which  may  be 
considered  as  the  armature,  comes  in  actual  contact  with 
the  polar  surfaces,  the  greater  the  relative  surfaces,  the 
j— 1  greater  will  be  the  at- 

traction ;  but,  after 
actual  contact,  the  at- 
traction is  greater  when 
the  polar  or  attracting 
surfaces  are  smaller. 

Consider  the  magnet 
in  Fig.  117.  When  the 
armature  is  in  actual 

FIG.  117. -Electromagnet  with  Flat-faced  Contact  with  the  Cores, 

and  Rounded  Core  Ends.  the  attraction  is  greater 

at  A  than  at  B.     This  may  be  explained  as  follows  : 
The  attraction  is  proportional  to 


I        I 


B 


144  SOLENOIDS 


Now,  £B=T-  (41) 

A. 


Hence, 

A2         A 

If  it  is  assumed  that  the  flux  (/>  is  constant,  it  will  be 
evident  that  the  smaller  the  value  of  A  the  greater  will 
be  the  attraction. 

67.    POLARITY  OF  ELECTROMAGNETS 

In  practice  the  exciting  coils  of  horseshoe  electro- 
magnets are  all  wound  in  the  same  direction.  After 
the  spools  are  mounted  on  the  yoke,  or  "  back  iron,"  the 
inside  terminals  of  the  coils  are  connected  together, 
leaving  the  outer  terminals  for  making  connection  to 
other  apparatus.  Sometimes  the  coils  are  connected  in 
multiple.  In  such  cases  the  inside  terminal  of  each 
coil  must  be  connected  to  the  outside  terminal  of  the 
other. 

A  little  reflection  will  show  why  the  above  methods 
are  necessary  in  order  that  both  coils  may  have  the 
proper  polarity.  The  relative  directions  of  current  and 
flux  are  shown  on  p.  24,  and  this  rule  may  be  applied  to 
coils  by  the  following  analogue.  Consider  the  direction 
in  which  an  ordinary  screw  is  turned  to  be  the  direction 
of  the  current,  and  the  direction  of  travel  of  the  screw 
to  be  the  direction  of  flux. 

68.    POLARIZED  ELECTROMAGNETS 

A  Polarized  Electromagnet  is  a  combination  of  a  per- 
manent magnet  and  an  electromagnet.  Normally  the 
whole  magnetic  circuit  is  under  the  influence  of  the 
permanent  magnet  alone.  When  a  current  flows 


ELECTROMAGNETS  WITH  ARMATURES         145 


through  the  coils  of  the  electromagnet,  the  polarity  of 
the  cores  due  to  the  permanent  magnet  may  be  aug- 
mented ;  partly  or  wholly  neutral- 
ized, or  even  reversed.  Figures 
118  and  119  show  how  the  polari- 
zation is  usually  effected.  In 
both  cases  the  armatures  and 
cores  are  of  soft  iron.  In  Fig. 
118  the  armature  is  pivoted  at  the 
center,  and  the  cores  are  con- 
nected to  a  soft-iron  yoke,  the 
whole  being  influenced  by  the 
permanent  magnet,  as  shown. 
This  type  is  extensively  used  in 
telephone  ringers.  The  type  il- 

lustrated    in    Fig.    119    is    that  FlG.118._Pola,,zedStriker 
commonly  used  in  telegraph  ap-  Electromagnet, 

paratus.    In  this  case  the  armature  is  pivoted  at  one  end. 


FIG.  119.  — Polarized  Relay. 

In  another  type  the  winding  is  placed  upon  the  soft- 


146 


SOLENOIDS 


iron  armature  which  oscillates  between  permanent  mag- 
nets. In  the  bi-polar  telephone  receiver  the  permanent 
magnet  is  also  the  yoke  for  the  electromagnet,  and  the 
diaphragm  is  the  armature.  In  Figs.  120  and  121  the 

armatures  are  permanent  mag- 
nets. These  give  a  general 
idea  of  the  action  of  polarized 
electromagnets.  Owing  to  the 
fact  that  like  poles  repel  while 
unlike  poles  attract  one 
another,  it  is  readily  seen  that 
when  the  electromagnet  is  ex- 
cited, one  of  its  poles  will  be 
.IV  and  the  other  S;  therefore, 
the  armature  will  be  attracted 
and  repelled  on  the  other,  this  action 
the  polarity  of  the  electromagnet. 


FIG.  120.  — Polarized  Electro- 
magnet. 


on   one   side 

depen  iing    upon 

Hence,  the  position  of  the  armature  is  controlled  by  the 

direction  in  which  the  current  flows  through  the  coils. 

Polarized  electro- 
magnets are  very  sen- 
sitive, respond  to 
alternating  currents, 

\ 


and  may  be  worked 
with  great  rapidity, 
—  the  synchronous 
action  depending 
upon  the  inertia  of 
the  armature.  The 


I/A  \ 


FIG.  121.  — Polarized  Electromagnet. 


armature  may  also  be  biased,  by  means  of  a  spring,  for 
use  with  direct  currents,  which  action  is  extremely 
sensitive.  This  practice  is  common  in  connection  with 
relays  used  in  wireless-telegraph  calling  apparatus. 


ELECTROMAGNETS   WITH   ARMATURES         147 


When  it  is  desired  to  balance  the  armature  of  a 
polarized  electromagnet  so  that  the  armature  may  be 
moved  in  either  direction,  at  will,  according  to  the 
direction  of  the  current,  the  device  in  Fig.  122  may  be 
employed.  The  field  of  the  per- 
manent magnet  tends  to  normally 
hold  the  armature  in  a  balanced 
position. 

The  great  sensitiveness  of  polar- 
ized electromagnets  as  compared 
with  those  which  are  non-polarized 
is  because  of  the  greater  change 
in  flux  density.  All  other  condi- 
tions being  equal,  the  attraction  FIO.  122. -^pTiaTized  Eiec- 
is  proportional  to  662.  Hence,  if  tromagnet. 

under  the  influence  of  the  permanent  magnet  alone 
£&=  1000,  £B2  =  1,000,000.  If  now  the  electromagnet 
alone  produces  a  flux  density  &&  —  5,  £B2  =  25.  "With 
the  complete  polarized  electromagnet,  however,  the 
total  flux  density  after  the  current  flowed  would  be 
6B=1005  and  6£2=  1005  2=  1,010,025,  an  increase  in 
attraction  proportional  to  1,010,025  - 1,000,000  =  10,025. 
Hence,  in  this  case,  the  polarized  electromagnet  would 
have  401  times  as  great  an  attraction  for  a  change  of  5 
lines  per  square  centimeter  as  would  be  obtained  with 
the  electromagnet  alone.  The  above  results  could, 
however,  only  be  obtained  under  ideal  conditions. 


CHAPTER   X 

ELECTROMAGNETIC  PHENOMENA 
69.    INDUCTION 

IF  a  conductor  be  passed  through  a  magnetic  field  at 
an  angle  to  the  lines  of  force,  an  e.  m.  f.  will  be  gener- 
ated in  the  conductor.  A  similar  effect  may  be  obtained 
by  varying  the  intensity  of  the  magnetic  field,  the 
conductor  remaining  stationary.  The  maximum  e.  m.  f. 
will  be  obtained  when  the  conductor  is  perpendicular 
to  the  lines  of  force,  and  when  the  intensity  of  the 
magnetic  field  is  suddenly  changed  from  zero  to  maxi- 
mum, or  vice  versa. 

This  is  the  principle  employed  in  all  dynamo-electric 
machines  and  transformers,  and  the  phenomenon  is 
known  as  Induction. 

A  similar  action  takes  place  between  two  wires 
arranged  side  by  side,  or  between  two  coils  of  wire 
placed  one  over  the  other,  when  one  of  the  circuits  is 
energized  with  a  current  varying  in  strength.  This  is 
due  to  the  varying  flux  produced  by  the  varying  cur- 
rent cutting  the  adjacent  conductor. 

•  The  rule  expressing  the  relative  directions  of  the  in- 
ducing and  induced  currents  is  known  as  Lenz's  law, 
and  is  as  follows  :  The  currents  induced  in  an  electric 
circuit,  by  changes  of  the  current  in,  or  of  the  position  of, 
an  adjacent  circuit  through  which  a  current  is  flowing, 
are  always  in  such  a  direction  as  ly  their  action  on  the 
inducing  circuit  to  oppose  the  change. 

148 


ELECTROMAGNETIC   PHENOMENA  149 

70.    SELF-INDUCTION 

When  there  is  a  change  in  the  strength  of  current  in 
a  conductor,  the  change  in  flux  produced  by  that  current 
establishes  a  counter-e.  in.  f.  in  the  conductor,  and 
this  phenomenon  is  called  Self-induction.  Thus,  in  a 
straight  conductor,  or  coil  of  wire,  if  the  current 
strength  increases,  the  increasing  flux  generates  a 
counter-e.  m.  f.  which  opposes  the  increasing  e.  m.  f., 
which  causes  the  increasing  current  ;  whereas,  if  the 
current  be  decreasing  in  strength,  the  e.  m.  f.  of  self- 
induction  acts  in  the  opposite  direction. 

The  presence  of  iron  in  the  magnetic  circuit  greatly 
increases  flux,  and  when  the  electric  circuit  is  suddenly 
interrupted,  the  e.  m.  f.  of  self-induction  often  becomes 
very  great,  producing  a  large  spark  at  the  point  of 
rupture.  This  principle  is  taken  advantage  of  in 
electric  ignition  apparatus. 

The  magnetic  field  acts  as  a  reservoir  of  magnetic 
energy  which  returns  to  the  electric  circuit  an  amount 
of  energy  corresponding  to  the  electrical  energy  re- 
quired to  establish  the  magnetic  field. 

The  practical  unit  of  self-induction  is  the  Henry,  and 
is  equal  to  109  absolute  units.  The  self-induction  in 
henrys  of  any  coil  or  circuit  is  numerically  equal  to  the 
e.  m.  f.  in  volts  induced  by  a  current  in  it,  changing  at 
the  rate  of  one  ampere  per  second. 

The  term  Flux-turns  (symbol  <$N)  is  conveniently 
given  to  the  product  of  the  total  flux  in  the  magnetic 
circuit  into  the  number  of  turns  in  the  exciting  coil. 

Inductance  (symbol  L)  is  the  coefficient  of  self-induc- 
tion. 


150  SOLENOIDS 


whence  £JV=  LI  x  108.  (103) 

As  an  example  :  if  a  coil  have  100  turns  of  wire, 
through  which  a  current  of  3  amperes  is  flowing,  the 
ampere-turns  will  be 

IN=  3  x  100  =  300. 

If  300  ampere-turns  produce  200,000  lines  of  force, 
i.e.  </>  =  200  kilogausses,  the  flux-turns  will  be 

0jy=100  x  200,000  =  20,000,000,  or  2  x  10*. 

9  v  1  07  9 


If  the  current  of  3  amperes  dies  out  uniformly  in  one 
second,  then  the  induced  e.  m.  f.  is 

e  =  L  —  =  0.06667  x  3  =  0.200  volt. 

v 

L  is  a  constant  when  there  is  no  iron  or  other  mag- 
netic material  in  the  magnetic  circuit.  When  iron  is 
present,  as  is  nearly  always  the  case  in  practice,  the 
permeability  for  different  degrees  of  magnetization 
must  be  taken  into  consideration. 

71.    TIME-CONSTANT 

The  phenomenon  of  self-induction  prevents  a  current 
from  rising  to  its  maximum  value  instantly,  i.e.  a  cer- 

W 

tain  lapse  of  time  is  required  before  Ohm's  law,  1=  —  , 

holds,  unless  the  effects  of  self-induction  be  neutralized. 

The  time-constant  is  numerically  equal  to  —  and  is 

R 

the  time  required  for  the  current  to  rise  to  0.634  or 
63.4  per  cent  of  its  Ohm's-law  value. 


ELECTROMAGNETIC   PHENOMENA  151 

Helmholtz's  law  expresses  the  current  strength  at  the 
end  of  any  short  time,  £,  as  follows: 

(104) 

wherein    e  =  2.7182818,    the   base    of    the    Napierian 
logarithms. 

Substituting  —  for  t  in  (104), 
R 

1=1(1-,-}  (105) 

Multiplying  and  dividing  the  right-hand  member  by 
e,  we  have 


Hence,  7=0.634^.  (107) 

jft 

From  the  above  it  is  seen  that  the  time-constant  may 
be  decreased  by  decreasing  the  inductance,  or  by  in- 
creasing the  resistance.  If  there  was  no  inductance, 
but  with  any  value  for  resistance,  the  current  would 
reach  its  Ohm's-law  value  instantly.  On  the  other 
hand,  if  there  was  no  resistance,  but  with  any  value  for 
inductance,  the  current  would  gradually  rise  to  infinity, 
the  relation  between  time  and  current  being 

7=  —  (108) 

L 

The  inductance  is  sometimes  called  the  electrical 
inertia  of  the  circuit. 

As  an  example,  assume  E  —  20  ;  R  =  500  ;  L  =  10. 
The  final  value  of  /will  be  -g2^  =  0.04  ampere,  and 


152  SOLENOIDS 

the  time-constant  is  ^^==0.02  second;  that  is,  the 
time  required  for  the  current  to  rise  to  0.04  am- 
pere x  0.634=  0.02536  ampere,  will  be  0.02  second. 

72.    INDUCTANCE  OF  A  SOLENOID  OF  ANY  NUMBER 
OF  LAYERS 

Louis  Cohen  has  deduced  a  formula*  which  is  correct 
to  within  one  half  of  one  per  cent  where  the  length  of 
the  solenoid  is  only  twice  the  diameter,  the  accuracy 
increasing  as  the  length  increases. 

The  formula  is  as  follows  : 


\  [(«  -  IX2  +  (n  -  2)r,«  +  •  -  ]  [  V^fTT'  -  J  r,] 
\  [n(n  -  T)r*  +  (n  -  l)(n  -  2)r* 


wherein        n  =  number  of  layers, 

r  =  mean  radius  of  the  solenoid, 
rv  r2,  r8,  •••  rn  =  mean  radii  of  the  various  layers, 
L  =  length  of  the  solenoid, 
d1  =  radial   distance   between   two  consecu- 

tive layers, 
m  =  number  of  turns  per  unit  length. 

All  the  above  are  expressed  in  centimeters. 

For  a  long  solenoid,  where  the  length  is  about  four 
times  the  diameter,  only  the  first  two  members  of 
equation  (109)  need  be  used,  i.e.  the  formula  ends 
with-frj. 

*  Electrical  World,  Vol.  L,  1907,  p.  920. 


ELECTROMAGNETIC   PHENOMENA  153 

The  above  is  for  a  solenoid  with  an  air-core. 
Maxwell's    formula,  while  not   so  accurate,  is  very 
convenient  for  rough  calculations,  and  is  as  follows : 

L  =  f  7r%4Z(re  -  rt-)(re»  -  r  3),  (110) 

wherein  re  and  r,-  are  the  external  and  internal  radii  of 
the  solenoid. 

73.    EDDY  CURRENTS 

Electric  and  magnetic  circuits  are  always  interlinked 
with  one  another.  The  current  in  a  coil  of  wire  sur- 
rounding a  bar  of  -magnetic  material  establishes  a 
magnetic  field  which  is  greatly  augmented  by  the  per- 
meability or  multiplying  power  of  the  magnetic  ma- 
terial. 

When  a  variation  in  the  strength  of  current  in  the 
coil  takes  place,  there  will  be  a  corresponding  variation 
(when  the  core  is  not  saturated)  in  the  strength  of  the 
magnetic  field  of  the  iron,  and  since  the  iron  or  steel 
constituting  the  core  is  a  conductor  of  electricty,  an 
e.  in.  f.  will  be  established  in  it  at  right  angles  to  the 

o  o 

direction  of  the  flux  in  the  core ;  that  is,  there  will  be 
mutual  induction  between  the  varying  current  in  the 
coil  and  the  iron  core. 

These  induced  currents  are  called  Eddy  Currents,  and 
are  largely  overcome  by  subdividing  the  core  in  the 
direction  of  the  flux.  By  this  method  the  path  of  the 
flux  is  not  interfered  with,  but  the  electric  circuit  in 
the  core  may  be  destroyed  to  a  sufficient  degree  for  all 
practical  purposes. 


CHAPTER   XI 


ALTERNATING  CURRENTS 
74.    SINE  CURVE 

IN  an  alternating-current  generator  of  the  type  de- 
picted in  Fig. 
123,  the  e.  in.  f. 
will  vary  as 
the  sine  of  the 
angle  through 
which  the  con- 
ductor travels 
through  the 
magnetic  field, 
the  rate  of  travel 
and  the  strength 
of  field  being 
uniform. 

Referring  to  Fig.  124,  it  is  evident  that  the  e.  in.  f. 
will   change   from    zero,  ° 

at  0°,  to  its  maximum 
value  at  90°,  and  will 
then  fall  to  zero  again  at 
180°.  The  same  opera- 
tion will  be  repeated  as 


i ^. 

FIG.  123.  — Production  of  Alternating  Current. 


the    conductor    revolves 


n  . 

FIG.  124.  —  Relative  Angular  Positions 


from    180°    to    360°,    but  of  Conductor. 

the  direction  of  the  e.  in.  f.  will  be  reversed. 

164 


ALTERNATING  CURRENTS  155 

The  instantaneous  values  of  the  e.  m.  f.  maybe  plotted 
in  the  form  of  a  curve,  as  in  Fig.  125.  This  is  known 
as  the  Sine  Curve  or  Sinusoid. 

One  complete  revolution  is 
called  a  Cycle  (symbol  ~),  and 
one  half  of  this  one  Alternation. 


Hence,  one  cycle  consists  of  two 

FIG.  125.  — Smusoid. 

alternations. 

The  Period  of  an  alternating  current  is  the  time  re- 
quired to  complete  one  cycle.  The  number  of  cycles 
per  second  is  the  Frequency  (symbol  /) .  In  this  country 
(U.S.A.)  the  standard  frequencies  are  25  ^  and  60  ~. 

75.   PRESSURES 

Referring  to  Fig.  125  it  is  seen  that  the  e.  m.f.,  dur- 
ing one  alternation,  is  Maximum  at  90°  or  270°,  and  that 
the  Average  or  Arithmetical  Mean  e.  in.  f.  is  proportional 
to  the  average  ordinate  of  the  curve. 

If  the  maximum  ordinate  at  90°  (or  270°)  be  consid- 
ered as  1,  then  the  area  of  the  curve,  for  one  alternation, 
is  2.  The  length  0°  to  180°  =  TT. 

Since  the  arithmetical  mean  e.  m.  f.,  EA,  is  propor- 
tional to  the  mean  ordinate, 

EA  =  -E=$.QZ1  E,  (111) 

7T 

for  the  positive  half -wave,  and  —  0.637  for  the  negative 
half-wave.  As  these  two  quantities  cancel  each  other, 
the  mean  e.  m.  f.  for  the  whole  wave  is  zero. 

The  Effective  Pressure,  Ee,  is  the  pressure  which  will, 
when  applied  to  a  non-inductive  resistance,  cause  a  flow 
of  current  which  produces  the  same  amount  of  heat  as 
the  corresponding  current  caused  by  a  direct  e.  m.  f.  of 


156  SOLENOIDS 

the  same  number  of  volts.  That  is,  an  effective  pres- 
sure of  one  volt  will  cause  an  alternating  current  of  one 
ampere,  effective  mean  value,  through  one  ohm  resist- 
ance; and  will  produce  heat  at  the  rate  of  one  watt. 
The  effective  pressure  is  equal  to  the  square  root  of  the 
mean  of  the  squares  of  the  successive  pressures  during  one 
alternation,  or 

=  \E  =  0.707  E.         (112) 

The  squares  of  negative  numbers  are  positive,  as  well 
as  those  of  positive  numbers;  therefore,  the  effective 
mean  values  are  all  positive,  and  the  effective  pressure 
is  the  same  for  the  whole  wave  as  for  the  half. 

From  the  preceding  equation,  it  follows  that 

H,  =  l.UJSA.  (113) 

Theeffective  e.  m.  f.  is  the  e.  m.  f.  referred  to  in  ratino- 

e> 

alternating-current  (A.  C.)  apparatus,  and  a  common 
commercial  pressure  is  104  volts. 

From  what  was  said  in  Art.  70,  it  is  evident  that 
there  will  also  be  a  counter-e.  m.  f.  due  to  inductance. 
This  is  called  the  Electromotive  Force  of  Self-induction 
(symbol  EL),  and  is  always  opposed  to  the  inducing 
force.  This  self-induced  pressure  is  the  greatest  when 
the  alternating  current  is  the  least,  and  vice  versa. 
That  is,  it  lags  90°,  or  one  quarter  of  a  cycle,  behind  the 
current.  The  current  itself  lags  behind  the  Impressed 
e.  m.  f.  any  amount  between  0°  and  90°,  according  to 
circumstances,  but  usually  in  practical  apparatus  con- 
taining inductances  purposely  introduced  (such  as  trans- 
formers and  choke  coils)  nearly  90°;  so  that  the  e.  m.  f. 
of  self-induction  lags  nearly  180°,  or  half  a  cycle,  behind 


ALTERNATING  CURRENTS 


157 


the  impressed  e.  m.  f.  That  is,  the  e.  m.  f.  of  self-induc- 
tion is  very  nearly  in  opposition  to  the  impressed  e.  m.  f . 
The  two  e.  m.  f.'s  are  then  said  to  be  out  of  phase  with 
each  other.  This  is  shown  in  Fig.  126. 


FIG.  126.  —  Impressed  e.  m.  f.  balancing  (nearly)  e.  m.  f.  of  Self-induction. 


The  Impressed  Pressure  (symbol  J5^),  when  applied  to 
a  circuit  containing  both  resistance  and  inductance,  is 
considered  as  being  split  up  into  two  components,  one 
of  which  is  in  opposition  to  and  balances  the  e.  m.  f.  of 
self-induction,  and,  therefore,  leads  the  impressed  e.  m.  f  . 
somewhat,  and  the  other,  called  the  Active  Pressure 
(symbol  J7a),  which  causes  current  to  flow,  and  which  is 
always  in  phase  therewith  and  proportional  thereto. 
The  component  which  balances  the  e.  m.  f.  of  self-induc- 
tion is  called  the  /Self-induction  Pressure  (symbol  Es). 
The  active  pressure  is  the  resultant  of  the  impressed 
and  self-induction  pressures. 


Therefore, 


(114) 


Referring  to  Fig.  127,  Ea  is  the  resultant  or  active 
pressure  required  to  send  the  current  /,  which  is  in  phase 
with  jEJa,  through  a  given  resistance,  and  Es  is  the  self- 
induction  pressure.  Curve  Ei  is  the  impressed  pressure 
or  applied  e.  m.  f.,  and  its  instantaneous  values  are  equal 


158 


SOLENOIDS 


to  the  algebraic  sums  of  the  instantaneous  values  of 
curves  Ea  and  Es.  It  is  somewhat  in  advance  of  / 
and  Ea. 

The  effective  value  of  the  induced   e.  m.  f.   may  be 


FIG.  127.  — Phase  Relations  when  Ea  =  Es. 

readily  calculated  when  the  inductance  L  is  known. 
<t>  is  the  maximum  flux,  and  this  is  cut  four  times  by 
the  coil  during  each  cycle,  since  the  flux  rises  from  zero 
to  maximum ;  falls  to  zero  ;  increases  to  maximum  in  the 
opposite  direction,  and  falls  again  to  zero.  Hence,  if 
the  coil*  has  N turns  and  the  frequency  is /cycles  per 
second,  the  average  or  arithmetical  mean  e.  m.  f.  will  be 


and  since  Ee  =  1.11  EA  (113), 

4.44 


108 

If  the  inductance  of  a  circuit  is  L  henrys, 


L= 


Im  X  108' 


(115) 
(116) 
(117) 


*  A  coil  as  in  Fig.  21,  p.  36,  is  here  meant.     For  inductance  due  to 
coil  of  any  dimensions,  see  Art.  72. 


ALTERNATING  CURRENTS  159 

wherein  Im  is  the  maximum  current,  which  will  be 

4  =  /,V2,  (118) 

wherein  Ie  is  the  effective  current. 

Therefore,  Je  =  A  =  0.707  Im.  (119) 

V2 

Hence,  L  =  ^-Jf  ^  (120) 


and  0^=  /eV2L  x  108,  (121) 

wherein  $N  =  flux-turns. 

But  from  (116) 

4  x  0/707        f  J^ 

^4-^F=        T         -*  ><  f  X^'  ^ 

7T 

Substituting  the  value  of  0  JVfrom  (121)  in  (122), 
1 


7T 

Hence,  -^4=2  7r/L/e.  (124) 

The  expression  2?r/  is  called  the  Angular  Velocity 
(symbol  o>). 

Representing  the  e.  m.  f.  of  self-induction  by  EL  and 
the  effective  current  by  /, 


(125) 
or  EL  =  coLL  (126) 


160  SOLENOIDS 

76.    RESISTANCE,   REACTANCE,   AND  IMPEDANCE 

The  expression  2  irfL  is  the  resistance  RL,   due  to 
self-induction,  and  is  known  as  Inductive  Reactance. 

Henoe'  J=    = 


The  apparent  resistance  offered  to  the  impressed 
e.  m.  f.  is  known  as  Impedance  (symbol  Z),  and  is  equal 
to  the  square  root  of  the  sum  of  the  squares  of  the  resist- 
ance and  reactance, 

or  Z  =  V^2  +  4  7r2/2L2.  (128) 

Then,  E{  =  IZ=  /V^2+4-7r2/2L2,  (129) 


Tjl 

and  1= 


+    4 

If  L  =  0, 

T-    EJ 

vi 

which  is  Ohm's  law. 

77.   CAPACITY   AND   IMPEDANCE 

The  Capacity  of  an  alternating-current  circuit  is  the 
measure  of  the  amount  of  electricity  held  by  it  when 
its  terminals  are  at  unit  difference  of  potential. 

An  example  of  capacity  is  found  in  the  familiar  type 
of  electrical  condenser,  in  which  sheets  of  tin-foil  are  in- 
_  ___^        sulated  from  one  another  and  arranged 
_    as  in  Fig.  128. 

The  effect  of  capacity  is  directly 
FiG.i28.-Coudeuser.   opposed  to   self-mduction,  and   it  is 

possible,  by  properly  adjusting  the  capacity  and  induc- 
tance  of   a   circuit   so   that   they   will   neutralize    one 


ALTERNATING  CURRENTS  161 

another,  to  bring  the  laws  of  the  alternating  current 
under  those  of  direct. 

If  Ec  be  the  pressure  applied  to  a  condenser  and  C  be 
its  capacity  in  Farads, 

I=27rfCEc,  (132) 

or  I=a>CEc,  (133) 

and  EC  =  -L.  (134) 

From  (134)  it  is  evident  that  the  resistance  due  to 
capacity  is 


ft 

w(J 

The  impedance  due  to  resistance  and  inductance  in 
series  was  given  in  equation  (128).    This  may  be  written 

Z=  V722  +  L2&>2.  (136) 

The   impedance    due  to  resistance  and  capacity  in 
series  is 


and  for  resistance,  inductance,  and  capacity  in  series 

(138) 


Co,}' 
78.    RESONANCE 
When   L&>  =  — ,  Z=R.     This   condition   is    called 

Resonance.*     This  effect  is  shown  in  Fig.  129. 

The    practical    unit   of   capacity   is    the    Microfarad 
(one  millionth  of  a  farad). 

*  For  further  particulars  see  Foster's  Electrical  Engineers1  Pocket 
Book. 


162  SOLENOIDS 


For  resonance,  L«  =  -   "";       ,  (139) 

&)Gr 


m 


wherein  Cm  is  the  capacity  in  microfarads. 

From  (139) 


(140) 

Since 

«=2*cf,  (141) 


Fia.  129.  —  Conditions  for  /  =  ~ —  \  F7T '        0- 4 2] 

Resonance.  m 

or  /=159.2^— L.  (143) 

The  opposing  capacity  and  inductance  e.  m.  f.'s 
usually  set  up  local  pressures  much  greater  than  the 
impressed  pressure. 

The  e.  m.  f.  at  the  terminals  of  an  inductance, 
necessary  to  force  a  current  through  it,  is 

J?Z  =  &>L7,  (126) 

and  since,  for  resonance, 

*  =  !,  (131) 

(144) 

Xt 

The  e.  m.  f.  necessary  to  force  a  current  through  a 
capacity  is 


ALTERNATING  CURRENTS 


163 


Substituting  —  for  I  in  (146), 


(147) 

As  an  example,  refer  to  the  conditions  shown  in  Fig. 
#=6"  OHMS 


-4         o> 


Z 


5 

o      *= 

0 

>         c 

i* 

o      g 

^ 

^        c 

I 

K-3070   VOLTS' 

*     I 

\ 

L_—  1 

C»  =  /5  MICRO-FAKflDS 

FIG.  130.  — Effects  of  Resonance. 


130.     Here  L  =  0.47,    (^=15,  ^=104,  72  =  6,  /=  60 
cycles,  Z=  lg-i=  17.3  amperes. 


From  (144) 
Since 


a>  =  2  TT/, 

104x27rx60x0.47 
6 


=  3070  volts, 


which  is  the  e.  m.  f.  across  the  terminals  of  the  induc- 
tance. 

The  e.  m.  f.  at  the  terminals  of  the  capacity  is 


(147) 


164  SOLENOIDS 

1,000,000  x  104 

Hence,         Ec  =  -  -  =  3070  volts. 

6  x  2  TT  x  60  x  15 

If  the  resistance  R  was  5  ohms,  the  e.  m.  f.'s  across 
the  terminals  of  the  inductance  and  condenser  would 
each  be  3675  volts  for  resonance.  Hence,  it  is  seen  that 
the  smaller  the  resistance,  the  greater  will  be  the  local 
e.  m.  f.'s. 

In  practice,  so  exact  values  cannot  be  obtained  owing 
to  the  fact  that  the  e.  m.  f.  is  not,  as  a  rule,  a  pure  sine 
curve  function,  as  has  been  assumed  in  the  foregoing. 
Although  complete  resonance  may  not  be  obtained, 
in  practice,  at  commercial  frequencies,  the  partial 
neutralization,  due  to  the  placing  of  capacity  and  in- 
ductance in  series,  tends  to  make  the  local  e.  m.  f. 
higher  than  the  impressed. 

79.    POLYPHASE  SYSTEMS 

When  the  angle  of  lag  between  two  currents  is  zero, 
they  are  in  phase.  If  the  angle  of  lag  is  90°,  they  are 

in  quadrature,  and  if  180°,  they 
are  in  opposition. 

In  Fig.  131  are  shown  two 
current  waves  in  quadrature. 
FIQ.  131.— Two-phase  Currents.  If  each  of  these  currents  were 
fed  into  separate  lines,  a  two-phase  system  would  be 
obtained  ;  the  currents  differing  in  phase  by  90°  or  one 
quarter  period. 

In  three-phase  systems  the 
currents    differ    in    phase    by  "          /"" X/^X/' \ 
120°  (one  third  period).     This       J      .xV-XX^ 

effect    is    shown    in    Fig.    132.      FIG.  1.32.  —  Three- phase  Cur- 
It  is  an  easily   demonstrated  rents< 


ALTERNATING  CURRENTS 


165 


property  of  these  currents  that  their  algebraic  sum,  at 
any  given  instant,  is  zero,  or,  in  other  words,  at  any 
given  instant,  there  is  one  of  the  three  currents  which 
is  equal  in  strength  to  the  sum  of  the  other  two  cur- 
rents, and  opposite  in  direction  thereto.  Consequently, 
one  wire  of  each  of  the  three  circuits  may  be  dispensed 
with,  and  the  three  currents  carried  on  the  three  remain- 
ing wires,  one  of  which,  at  any 
given  instant,  acts  as  the  return 
for  the  other  two,  or  two  act  as 
the  return  for  the  other  one. 

The  general  plan  of  the  two- 
phase  system  is  shown  in  Fig.  133, 
while  the  two  common  three- 
phase  systems  are  diagrammatic- 
ally  shown  in  Figs.  134  and  135, 

the  former  being  called  the  Star 
or  Y  connection  and  the  latter 
the  Delta  (A)  connection. 


FIG.  133.  — Two-phase 
System. 


FIG.  134.  — Star  or  Y  Connec-    FIG.  135.— Delta  Connection,  Three-phase, 
tion,  Three-phase. 

80.    HYSTERESIS 

When  an  alternating  current  flows  through  the 
winding  of  an  electromagnet,  the  magnetism  in  the 
core  is  rapidly  and  completely  reversed,  the  magnetiz- 
ing force  rising  from  zero  to  maximum ;  falling  to 
zero ;  then  to  its  maximum  value  in  the  negative  direc- 
tion, and  back  again  to  zero. 


166  SOLENOIDS 

Theory  indicates  that  the  molecules  of  the  magnetic 
material  in  the  core  are  reversed  with  each  reversal  of 
the  magnetizing  force,  and  that  a  certain  molecular 
friction  takes  place  which  is  due  to  the  coercive  force 
in  the  magnetic  material.  This  friction  causes  a  loss 
of  energy  in  the  form  of  heat.  The  phenomenon  is 
known  as  Hysteresis,  and  the  energy  loss  as  the  Hys- 
teresis Loss. 

The  Hysteresis  Loop  in  Fig.  136  shows  the  relative 
values  for  BS  and  £&  in  a  soft-iron  ring.  When  the 
iron  was  first  gradually  magnetized,  the  curve  started 
from  the  origin,  but,  owing  to  the  coercive  force,  the 
curve  can  never  again  pass  through  the  origin  after  the 
iron  is  once  magnetized.  The  hysteresis  loss  is  pro- 
portional to  the  area  of  the  hysteresis  loop. 

Steinmetz,  after  exhaustive  experiments,  has  found 
this  loss  to  be 

wc  =  A^-s,  (148) 

wherein       wc  =  watts  lost  per  cubic  centimeter  of  iron, 

/=  number  of  complete  reversals  (cycles) 

per  second, 

and  nc  =  hysteretic  constant, 

which  varies  with  different  grades  of    iron  and  steel, 
0.003  being  a  good  average  for  thin  sheet  iron. 


ALTERNATING   CURRENTS 


167 


FIG.  136.  —  Hysteresis  Loop. 


CHAPTER  XII 


ALTERNATING-CURRENT  ELECTROMAGNETS 
81.    EFFECT  OF  INDUCTANCE 

IN  an  alternating-current  (A.  C.)  electromagnet,  the 
inductance  will  vary  with  the  relative  positions  of  the 


//    CMS. 


coil 


FIG.  137.— A.  C.  Solenoid. 

and  plunger  or  armature.      Hence,  the  strength  of 

the  current  will  vary 
also.  To  illustrate 
this  effect,  some  tests  * 
made  by  the  author 
will  be  cited. 

The  solenoid  in  Fig. 
137  was  tested  with  a 
core   or   plunger  con- 
sisting of  a  bundle  of 
soft-iron     wires,     and 
Fig.  138  shows  a  result 
of  a  test  of  this  sole- 
noid on  a  104-volt,  60- 
*  American  Electrician,  Vol.  XVII,  1905,  p.  467. 
168 


3 

H 

^    2 

•1 

wj 

0 

FIG. 

/ 

13.5 

V 

u 
4 

3.0    £ 

5 

1 

/ 

<J 

^ 

**" 

2         4        6         0        /» 

LE(i&TH  Of  fit  ft  -CORE     (C/V«S) 

138.  —  Characteristics  of  A.  C.  Sole- 
noid. 

ALTERNATING-CURRENT   ELECTROMAGNETS     169 


cycle  circuit.  It  will  be  noticed  that,  as  the  plunger  is 
withdrawn,  the  current  increases,  thereby  increasing  the 
ampere-turns,  and  consequently  the  pull  on  the  plunger. 


/5  CMS 


/8.5    CMS. 


FIG.  139.  —  Inductance  Coil  with  Taps. 

The  coil  in  Fig.  139  has  a  laminated  core  and  also  three 
taps,  making  four  test 
windings.  The  resist- 
ances were  0.11,  0.23, 
0.36,  and  0.63  ohm,  j» 
respectively,  and  the 
turns  131,  261,  388, 
and  609,  respectively. 
Figure  140  shows  the 
resistance  and  turns 
and  the  corresponding 
current  on  104  volts 
and  60  cycles.  This 


r—  <WOj 
-    0.55 
—   0.50 

3~ 
\ 

/ 

pH 

-w  0.35 
-3  0.30 

2aa 

-r° 

-.00.15 

/  - 

\ 

5 

ss 

\ 

\ 

-/ 
/ 
/ 

-    0.10 
-    0.05 

_X 

=     i 

^<?- 

? 

.>:> 
1 

2 

§ 

to 

\ 

Ti 

* 

3 

rns 

*&- 

I 

1 

§  ' 

•\ 

?  c 

?  p 

FIG.  140. — Characteristics  of  Inductance 
Coil  with  Taps. 


also  shows  the  ratio  between  resistance  and  impedance 
for  different  numbers  of  turns. 


170  SOLENOIDS 

The  curves  in  Fig.  141  are  plotted  from  a  test  of  the 
entire  winding  of  609  turns  and  0.63  ohm,  and  show 

the    effect  of   inserting 
1 1   different  proportions  of 
•  the  total  amount  of  the 
iron  wires  constituting 


J4        X        K       X        K       36 
Proportion  of  Iron  Wires  in  Core.  tllC    COrC,     wllicll    WaS     19 


FIG.  141.  —  Effect  due  to  Varying  Iron  in    cm.  lonp-  and  3.8  cm.  in 
Core.  ,  . 

diameter. 

The  test  plotted  in  Fig.  140  shows  that  while  the 
resistance  in  the  winding  was  only  0.63  ohm,  the  total 

impedance  was  —  —  =  69.4   ohms,   making   the   resist- 
1.5 

ance  of  the  copper  in  the  winding  practically  a  neg- 
ligible factor. 


82.    INDUCTIVE  EFFECT  OF  A.  C.  ELECTROMAGNET 

The  constantly  changing  flux  which  sets  up  an  e.  m.  f . 
of  self-induction  also  tends  to  induce  currents  in  the 
cores,  frame,  and  other  metallic  parts  of  the  magnet. 
These  induced  currents  oppose  the  current  in  the  coil 
and  resist  any  changes  in  the  magnetism.  This  is  in 
accordance  with  Lenz's  law.  (See  Art.  69,  p.  148.) 

The  natural  method  of  reducing  these  induced  or 
secondary  currents  is  to  subdivide  the  core  at  right 
angles  to  the  direction  of  the  flux.  Thin  laminae,  in- 
sulated from  one  another,  are  employed. 

If  the  spool  be  of  metal,  it  should  be  slotted  longi- 
tudinally with  one  slot  through  the  tube  and  washers. 
This  general  rule  should  be  followed  for  all  metal  parts. 

In  an  A.  C.  solenoid  or  plunger  electromagnet,  the 
flux  tends  to  pass  through  the  metal  (usually  brass) 


ALTERNATING-CURRENT   ELECTROMAGNETS    171 

tube,  in  which  the  plunger  travels,  at  an  angle  with 
the  direction  of  travel.  Hence,  the  tube  is  liable  to  be 
heated  at  the  position  of  the  end  of  the  plunger,  unless 
a  great  many  slots  are  milled,  or  holes  bored,  in  the 
tube.  This  effect  is  even  more  marked  at  the  mouth 
of  the  plunger  electromagnet,  where  the  flux  passes 
from  the  frame  to  the  plunger. 


FIBRE 


83.    CONSTRUCTION  OF  A.  C.  IRON-CLAD 

SOLENOIDS 

In  Fig.  142  is  shown  the  proper  form  of  iron-clad 
solenoid,  for  the  elimination  of  noise.  By  this  con- 
struction, the  noise  or 
chattering1  due  to  the 

O 

striking  of  the  plunger 
against  the  iron  frame 
at  each  alternation  is 
eliminated. 

In  any  type  of  A.  C. 
electromagnet,  the 
plunger,  cores,  or  arma- 
ture, though  laminated, 
must  be  solidly  con- 
structed so  that  there 
can  be  no  lateral  vibra- 
tion of  the  lamiiue,  as 
otherwise  humming 
would  result.  There 

is    also   a    tendency    Oil     FlG-  142.  — Method  of  Eliminating  Noise 
.,  ,,    ,,  in  A.  C.  Iron-clad  Solenoid. 

the  part  of  the   plun- 
ger to  vibrate  sidewise,  where  it  passes  through  the  iron 
frame,  which  may  be  avoided  by  using  a  guide   and 


172 


SOLENOIDS 


making  the  hole  through  the  frame  considerably  larger 
than  the  core. 

When  the  cores  or  plungers  are 
built  up  of  thin  sheet  iron,  they  are 
usually  square  in  cross-section  or  of 
the  form  shown  in  Fig.  143,  while 
those  made  of  iron  wires  are  round. 

The  ^P6  of  Core  shown  in 

is  for  use  in  a  round  tube. 


FIG.  143.-Laminated 

Core. 


84.    A.  C.  PLUNGER   ELECTROMAGNETS 

The  frame  and  plunger  of  the  single-coil  plunger 
electromagnet,  shown  in   Fig.   144,  are  constructed  of 


o 


FIG.  144.  —  A.  C.  Plunger  Electromagnet. 


FIG.  145.  —  Two-coil  A.  C.  Plunger  Electromagnet. 


ALTERNATING-CURRENT   ELECTROMAGNETS       173 


174  SOLENOIDS 

thin  iron  laminae  riveted  together.  While  this  is 
easily  constructed  after  the  punches  and  dies  are 
made,  it  is  rather  expensive  to  make  without  the 
above  special  tools.  Hence,  where  it  is  intended  for 
intermittent  work,  the  frame  often  consists  of  a  solid 
casting. 

The  frame  and  plunger  of  the  two-coil  plunger  elec- 
tromagnet in  Fig.  145  consists  of  two  U-shaped,  lami- 
nated parts,  upon  one  of  which  the  spools  are  mounted. 
This  is  a  simple  form  of  construction.  The  results  of 
a  test  *  of  this  magnet  by  the  author  on  a  104-volt,  60- 
cycle  circuit  is  shown  in  Fig.  146. 

Each  spool  was  wound  with  1400  turns  of  No.  20 
B.  &  S.  wire,  and  connected  in  parallel.  From  Fig. 
146  it  is  seen  that  while  the  current  is  very  strong  at 
the  beginning  of  the  stroke,  it  falls  to  a  low  value  after 
the  magnet  performs  its  work.  This  is  a  decided 
advantage. 

This  magnet  is  capable  of  a  much  stronger  pull,  with 
correspondingly  stronger  current,  but  it  was  designed 
for  nearly  continuous  service,  and,  therefore,  would 
overheat  if  the  impedance  were  made  lower. 

For  maximum  efficiency,  the  center  of  the  air-gap 
should  be  at  the  center  of  the  coil,  as  in  direct-current 
electromagnets. 

85.    HORSESHOE  TYPE 

This  magnet,  illustrated  in  Fig.  147,  is  easily  made 
from  the  U-shaped  laminae  described  in  Art.  84.  In 
the  design  of  these  cores,  great  care  must  be  exercised 
in  the  selection  of  the  proper  wire  or  laminae,  for  if 
the  wire  or  laminae  be  too  large  in  cross-section,  the 
*  American  Electrician,  Vol.  XVII,  1905,  pp.  467-468. 


ALTERNATING-CURRENT  ELECTROMAGNETS    175 


loss  due  to  eddy  currents  will  be  too  great ;  on  the 
other  hand,  if  the  wires  be  too  small  in  cross-section, 
or  the  insulation  between  them  be 
too  thick,  the  magnetic  reluctance 
will  be  so  great  as  to  more  than 
offset  the  evil  effects  of  the  eddy 
currents.  The  spools  are,  of  course, 
slotted,  if  of  metal. 

Whenever  it  is  feasible,  from  a 
mechanical     standpoint,     to     use  FIG.  147.  — A.  c. 
spools  of  insulating  material,  it  is 
electrically  advantageous  to  do  so,  as  the  induced  cur- 
rents in  the  spools  will  be  eliminated. 

86.    A.  C.  ELECTROMAGNET  CALCULATIONS 


From  (116) 


Horse- 
shoe  Electromagnet. 


108 


wherein  E  is  the  impressed  e.  m.  f.,  $  the  total  flux,  N 
the  number  of  turns  in  the  coil,  and/ the  frequency. 
Since  <   =  fj&A, 


(149) 


108 


On  account  of  the  heating  due  to  hysteresis  and  eddy 
currents,  A.  C.  electromagnets  are  usually  worked  at 
lower  flux  densities  than  for  D.  C.  magnets. 

The  exact  value  of  the  current  cannot  be  easily  calcu- 
lated, due  to  the  variable  induction  in  the  iron,  but  if 
a  curve  be  plotted  showing  the  magnetic  flux  for  each 
instantaneous  current  strength,  an  accurate  value  of  the 
effective  current  may  be  obtained. 

If  the  saturation  curve  is  considered  to  be  a  straight  * 

*  D.  L.  Lindquist,  Electrical  World,  Vol.  XL VII,  1906,  p.  1296. 


176  SOLENOIDS 

line  (which  is  nearly  correct  for  a  long  air-gap),  and 
the  current  at  the  begiriing  of  the  stroke  is  7,  then 


wherein  ^  is  a  constant. 

From  equations  (149)  and  (150) 


(15D 


(r$  4 
From  equation  (68)  P  = 


8  TT  x  981,000 
Transposing,  8&A  =  8  nrP  x  981,000.          (153) 

Substituting  the  value  of  &&A  from  (153)  in  (152), 
4.44  cP  xS     x  981,000 


If  1.095^  =  c2,  then 

(155) 


From  (154)  P  =  ~,  (15G) 

V 

which  shows  that  the  pull  decreases  as  the  frequency 
increases.  The  efficiency  of  the  magnet  also  varies 
with  the  frequency. 

87.    POLYPHASE  ELECTROMAGNETS 

Single-phase  electromagnets  may  be  operated  on 
polyphase  circuits  by  connecting  the  magnet  in  one 
of  the  phases  only,  or  magnets  corresponding  in  num- 
ber to  the  number  of  phases  may  be  connected  in  the 
respective  phases,  with  their  armatures  rigidly  con- 
nected to  a  common  bar  or  plate,  as  in  Fig.  148. 


ALTERNATING-CURRENT   ELECTROMAGNETS    177 


D.  L.  Lindquist  *  has  published  the  results  of  tests 
of   polyphase   magnets,    and    has   treated    the    matter 


FIG.  148.— Single-phase  Magnets  on  Three-phase  Circuit. 

thoroughly.     The  following  is  abstracted  from  his  ar- 
ticles. 

Figure  149  shows  a 
two-phase  magnet 
which  consists  of  two 
cores  practically  alike. 
Each  core  is  built  up 

P       i  -IT  FIG.  149.  —  Polyphase  Electromagnet. 

of  a  brass  spider,  5,  on 

which  is  wound  a  spiral  of  iron  band  (or  ribbon),  c ; 
between  consecutive  layers  of  iron  is  a  thin  sheet  of 
paper  fastened  with  shellac.  The  in- 
terconnection of  the  four  coils  of  the 
magnet  is  shown  in  Fig.  150. 

Assume    now    that    the    two-phase 

ir>o.  —  Connec-  e-  m>  f*'s  impressed  upon  the  core  are 
tions   of   Coils  of  in  time  quadrature  with  each  other, 

and  that  the  e«  m«  f'  WaVGS  are  °f  sin6 

shape.  Let  the  instantaneous  density 
in  cores  1  and  2  be  represented  by  6B«  and  that  in  cores 
3  and  4  by  t$b.  If  the  coil  resistance  and  the  magnetic 
leakage  are  negligible, 

*  Electrical  World,  Vol.  XL VIII,  1906,  pp.  128-130  and  564-567. 


178 


SOLENOIDS 


and 


,  where  K  is  a  constant,      (157) 
.  (158) 

(159) 


The  total  pull  is  proportional  to 


cos2  tot  = 


(160) 


Consequently,  the  pull  is  proved  to  be  constant  at 
any  tipie  and  equlal  to  tile  maximum  in  arij^  one  core. 
_  As    a    result    of    the 

construction  the  re- 
sultant pull  is  always 
exerted  through  the 
center  axis  of  the 
magnet,  thus  prevent- 
ing rocking  and  the 
consequent  chattering. 
That  a  three-phase 
magnet  having  three 
pairs  of  poles  also  gives 
a  constant  pull  can  be 
similarly  proved.  In 
practice,  however,  the 
two-phase  magnet  with 
two  pairs  of  poles  has 
been  found  suitable  for 
all  phases,  although  it 
gives  slightly  less  pull 
when  used  on  three-phase,  especially  with  small  air-gaps, 
as  indicated  in  Figs.  151  and  152,  which  show  tests  at 
60  cycles  on  a  certain  magnet  wound  with  four  coils, 
each  containing  220  turns  No.  14  wire,  the  cross-sec- 


100 


ISO 


PULL 

FIG.  151.  —  Two-phase  Electromagnet  sup- 
plied with  Two-phase  Current. 


ALTERNATING-CURRENT   ELECTROMAGNETS    179 


tional  area  of  the  core  being  12.5  sq.  cm.     For  large 
air-gaps  the  pull  is  practically  the  same  in  the  two  cases. 

As  previously  proved,  joo{ 
where  the  coil  resistance 
is  negligible,  and  the 
magnet  has  a  pair  of 
poles  for  each  phase,  a 
polyphase  magnet,  when 
energized  by  a  sine- 
shaped  e.  m.  f.,  exerts  a  ^ 
constant  pull.  As  a 
matter  of  fact,  however, 
in  almost  every  case  the  £ 
e.  m.  f.  is  more  or  less 
distorted,  due  to  many 
causes,  the  resistance 
having  a  certain  in- 
fluence, and  there  must 


750 


^o  /oo 

PULL    (K&*) . 

be  some  variation  in  the  FlG    152  _  Two.phase    Electromagnet 

pull.        If     a     two-phase        supplied  with  Three-phase  Current. 

magnet  is  used  on  a  three-phase  circuit,  there  will  be  an 
additional  variation  due  to  this  fact.  A  polyphase  mag- 
net should,  therefore,  never  be  loaded  to  such  an  extent 
that  the  load  exceeds  the  minimum  instantaneous  pull 
of  the  magnet. 

Suppose  that  the  load  is  in  excess  of  this  minimum, 
then  the  conditions  would  be  the  same  as  with  a  single- 
phase  magnet  ;  the  armature  would  leave  the  fixed 
pole  when  the  pull  was  less  than  the  load,  causing  a 
blow  when  returning.  The  total  pull  is  proportional  to 


e\  =  sin2a 


(161) 


180 


SOLENOIDS 


Hence,  if  the  average  pull  is  1,  the  maximum  pull  is  1.5, 
and  the  minimum  0.5. 

Figure  153  shows  the  results  of  tests  on  the  two- 


/oo 


125 


ISO 


PULL 
FIG.  153.— Test  of  Two-phase  Electromagnet  with  Three-phase  Current. 

phase  magnet  when  energized  with  three-phase  current, 
the  load  being  increased  until  the  magnet  made  a  noise. 
As  seen  from  these  curves  compared  with  Figs.  151  and 
152,  giving  the  pull  when  energized  with  two-phase  and 
three-phase  current,  the  magnet  will  commence  to  be 
noisy  at  about  one  half  the  load,  but  in  general  it  will 
hold  without  noise  all  the  load  it  can  lift,  so  long  as  the 
length  of  motion  is  not  too  short.  The  full  lines  indi- 
cate the  pull  at  which  the  magnet  begins  to  hum  at 


ALTERNATING-CURRENT   ELECTROMAGNETS    181 

various  voltages  with  different  air-gaps,  while  the  dotted 
lines  show  the  pull  at  which  chattering  begins. 

The  tests  above  referred  to  were  made  at  room  tem- 
perature, which  was  approximately  25°  C.  As  the  tem- 
perature increases  the  eddy  currents  decrease,  and  both 
the  current  and  the  total  losses  decrease  considerably, 
especially  for  zero  air-gap.  A  certain  test  was  made 
to  find  out  how  the  losses  and  current  consumption 
varied  at  different  temperatures.  A  magnet  was  ener- 
gized with  high  voltage  to  heat  the  coils  and  the  core. 
The  temperature  rise  of  the  core  was  57°  C.  and  of 
coils  69°  C. 

It  was  then  found  that  with  the  same  voltage  and 
zero  air-gap,  the  current  consumption  was  only  85  per 
cent  of  the  current  consumption  when  the  magnet  was 
at  the  room  temperature.  The  ohmic  resistance  of  the 
coils  increased  28  per  cent,  and  the  I2  R  losses  in  the 
coils  were  about  92  per  cent  of  the  losses  when  the  coils 
were  at  room  temperature.  The  total  losses  were  85 
per  cent  of  the  losses  when  the  magnet  was  at  room 
temperature.  As  the  I2  R  losses  in  the  coils  were  only 
about  35  per  cent  of  the  total  losses,  the  iron  losses 
when  hot  were  only  81.5  per  cent  of  the  iron  losses  at 
room  temperature,  due  to  decrease  in  eddy  currents. 
This  decreasing  of  the  losses  when  the  temperature  in- 
creases is  naturally  very  advantageous,  especially  for 
magnets  having  to  hold  their  loads  continuously. 

The  fact  that  the  pull  is  practically  independent  of 
the  coil  resistance,  as  long  as  this  resistance  is  fairly  well 
proportioned,  is  of  very  great  advantage  for  several  rea- 
sons. When  winding  the  coils  for  a  magnet  of  this 
kind  to  give  a  certain  pull,  no  definite  size  of  wire  is 
necessary  —  merely  the  right  number  of  turns  —  and 


182 


SOLENOIDS 


furthermore  the  temperature  of  the  coil  has  no  influ- 
ence on  the  pull.  Of  course,  the  coil  resistance  can 
be  increased  to  such  a  value  that  it  has  a  great  deal  of 
influence  on  the  pull,  but  then  the  coil  is  entirely  out 
of  proportion,  and  there  is  no  necessity  of  using  as 
small  a  wire  as  with  direct-current  magnets  because 
only  a  small  number  of  turns  is  necessary. 

In  general  neither  resistance  nor  inductance  of  a 
fixed  amount  can  be  used  for  regulating  the  voltage  on 
an  alternating-current  magnet.  If  inductance  or  resist- 
ance is  used  for  regulating  the  voltage,  it  is  used  in 
conjunction  with  a  switch  for  inserting  more  induct- 
ance or  resistance  after  the  magnet  has  lifted. 

It  is  impossible  to  make  a  single-coil  magnet  with 
constant  pull,  but  with  the  aid  of  two  external  resist- 
ances a  two-phase  magnet  can  be  arranged  to  give  con- 
stant pull  when  energized  with  single-phase  current. 

Figure  154  gives  the  connection  diagram,  while  Fig. 
155  shows  the  voltage  diagram  for  this  case.  All  coils 
are  wound  with  the  same  number  of 
turns,  and  in  order  to  obtain  constant 
pull,  it  is  necessary  that  all  coils  be 
energized  alike  or  that  the  voltage 
across  every  coil  be  the  same,  and  also 
that  the  e.m.f.'s  in  coils  1  and  3  are 
in  quadrature  to  the  e.m.f.'s  in  coils 
2  and  4.  The  cur- 
no.  154. -Connection  rent  through  coils  /.^ 

Diagram    for    Poly-    .  14  *'* 

1  and  3  must  natu- 


Resistance 


II 


wwwvwww" 
Resistance 


phase     Electromag- 
net on  Single-phase   rally  be  considerably 

Circuit<                    larger     than      that  Fl«-  ^5. -Phase  Re- 

,         .,     ~        ,  A  .           ,  lations  in  Polyphase 

through  coils  2  and  4  m  order  to  get  the  ElectromaKnet     on 

proper  phase  relation.     The  poles  of  Single-phase  Circuit. 


ALTERNATING-CURRENT   ELECTROMAGNETS    183 

coils  1  and  3  are,  therefore,  made  shorter  in  order  to  have 
a  certain  amount  of  air-gap  between  them  when  the 
plunger  is  in  the  up  position. 

In  order  to  obtain  the  required  starting  pull  (with 
the  plunger  in  the  lower  position  or  with  the  maximum 
air-gap)  only  a  small  amount  of  resistance  is  used,  and 
the  proper  resistance  for  holding  is  introduced  after  the 
magnet  reaches  its  final  position. 


CHAPTER   XIII 

QUICK-ACTING  ELECTROMAGNETS  AND  METHODS 
OF  REDUCING   SPARKING 

88.  RAPID  ACTION 

IT  has  been  shown  that  by  increasing  the  number  of 
turns  in  a  direct-current  magnet,  the  inductance  is  in- 
creased, which,  in  turn,  increases  the  time  of  energizing, 
and  also  the  time  of  deenergizing.  The  induced  cur- 
rents in  the  coiled  core  and  yoke  also  have  similar  ef- 
fects. Hence,  where  rapid  action  is  desired,  the  iron  and 
other  metal  parts  should  be  subdivided,  as  in  the  case 
of  alternating-current  magnets. 

As  the  time  constant  of  two  coils  connected  in  paral- 
lel is  only  one  fourth  of  what  it  would  be  were  they 
connected  in  series,  this  method  of  connection  is  desir- 
able for  rapid-acting  magnets. 

89.  SLOW  ACTION 

On  the  other  hand,  slow  action  is  sometimes  desirable. 
This  is,  of  course,  obtained  by  leaving  the  cores  and  yoke 
solid,  and  by  winding  the  wire  upon  a  heavy  solid  brass 
or  copper  spool.  When  the  spool  consists  of  insulating 
material,  the  retarding  effect  may  be  increased  by  either 
placing  a  brass  or  copper  sleeve  over  the  core,  or  by  the 
use  of  a  short-circuited  winding  which  is  separate  and 
distinct  from  the  regular  winding.  This  short-circuited 
winding  may  be  provided  with  taps,  by  means  of  which 
the  retarding  effect  may  be  varied. 

Figure  156  is  the  result  of  a  test  *  of  such  a  magnet. 

*D.  L.  Lindquist,  Electrical  World,  Vol.  XLVII,  1906,  p.  1295. 

184 


QUICK-ACTING   ELECTROMAGNETS 


185 


90.    METHODS  OF  REDUCING  SPARKING 

When  an  electromagnet  is  connected  in  a  circuit,  the 
phenomenon  of  inductance  tends,  upon  rupturing  the 
circuit,  to  increase  the 
total  e.  m.  f.,  thus  pro- 
ducing an  abnormal 
flow  of  current  mo- 
mentarily. This  prin- 
ciple is  in  common  use 
in  electric  ignition  ap- 
paratus, and  explains 
why  so  large  a  spark 
cannot  be  obtained 
when  a  very  short  con- 
tact is  made,  as  may  be 
obtained  witli  a  longer 
duration  of  contact. 

In  the  practical  ap- 
plication of  the  electro-  Fm   156_Retardation  Test  of  Direct. 

magnet    this    Sparking  current  Electromagnet. 

is  very  detrimental,  as  the  repeated  sparking  at  the 
point  of  rupture  rapidly  destroys  the  contacts. 

There  are  several  ways  of  reducing  the  sparking.  In 
one  method,  two  exactly  similar  insulated  wires  are 
wound  in  parallel  instead  of  one,  as  is  customary,  thus 
forming  two  complete  and  distinct  windings  thoroughly 
insulated  from  each  other,  but  lying  adjacent  to  each 
other  in  every  turn  of  the  winding.  The  two  terminals 
of  one  winding  are  then  connected  together,  thus  short- 
circuiting  the  winding  upon  itself.  The  other  winding 
is  used  as  the  regular  exciting  coil. 

If  now  a  current  be  suddenly  passed  through  the  ex- 
citing winding,  a  current  will  also  be  set  up  in  the 


2  3 

Time  in  Seconds 


186  SOLENOIDS 

short-circuited  winding.  In  this  case  the  effect  is 
electrostatic  as  well  as  electromagnetic,  since  the  two 
windings  lie  adjacent  throughout  their  entire  length  ; 
therefore,  there  will  be  no  extra  sparking  at  the  point  of 
rupture. 

In  order  to  obtain  this  result,  however,  it  is  necessary 
to  sacrifice  one  half  the  total  winding  space.  Hence  in 
some  cases  a  condenser  is  connected  across  the  point  of 
rupture,  which  condenser  should  have  sufficient  capacity 
to  absorb  all  of  the  extra  current  due  to  inductance. 
By  this  latter  arrangement,  all  of  the  winding  space 
may  be  utilized.  In  this  type,  the  condenser  is  some- 
times placed  around  the  outside  of  the  winding  in  order 
to  make  the  whole  magnet  compact  and  self-contained. 

Sometimes  the  condenser  is  placed  across  the  termi- 
nals of  the  electromagnet.  By  this  arrangement,  with 
proper  capacity  in  the  condenser,  the  sparking  due  to 
the  inductance  is  entirely  eliminated. 

In  neither  case  does  the  condenser  prevent  the  re- 
tarding action  of  the  coil,  as  in  the  former  case  the  con- 
denser is  short-circuited,  and  in  the  latter  it  is  not 
materially  affected  by  the  current  at  "make."  In  the 
former  case  the  contacts  are  subject  to  much  pitting, 
due  to  the  short-circuiting  of  the  condenser  at  "make." 

The  "  break  "  may  be  shunted  by  a  resistance  which 
is  usually  from  40  to  60  times  the  resistance  of  the 
winding  of  the  electromagnet,  according  to  the  condi- 
tions under  which  the  magnet  is  to  be  used. 

The  electromagnet  itself  is  also  often  shunted  by  a 
high  resistance  —  usually  a  rod  of  graphite  —  which 
should  have  about  20  times  the  resistance  of  the  coil. 
In  any  event,  the  resistance  for  this  purpose  must  be 
non-inductive. 


QUICK-ACTING  ELECTROMAGNETS  187 

The  "  break "  may  be  shunted  by  a  resistance  in 
series  with  a  battery  or  other  source  of  energy  which 
will  have  just  sufficient  e.  m.  f.  to  balance  the  e.  m.  f.  of 
the  working  circuit  across  the  break,  but  which  will 
provide  a  path  for  the  extra  current  at  the  high  poten- 
tial. See  Fig.  157. 


FIG.  157.  —  Resistance  and  E.  M.  F.  in  Series,  in  Shunt  with  "  Break." 

The  winding  may  also  be  short-circuited  instead  of 
opening  the  electric  circuit,  as  then  the  extra  current  is 
absorbed  in  a  closed  circuit,  and  there  will  be  no  sparking 
when  the  shunt  is  switched  out,  as  there  will  at  that 
instant  be  no  current  in  the  winding.  This  is  not  a 
very  economical  arrangement,  however,  and  it  is  obvious 
that  a  very  serious  short-circuit  of  the  battery  or  gener- 
ator would  occur  when  the  winding  of  the  electromagnet 
was  short-circuited,  unless  an  external  resistance  was 
provided  which  should  remain  in  circuit  after  the  wind- 
ing of  the  electromagnet  was  short-circuited. 

A  method  very  similar  to  that  first  described  is  known 
as  the  differential  method,  in  which  the  windings  of  the 
electromagnet  are  arranged  differentially,  as  in  Fig.  158. 
When  the  switch  is  open,  the  current  passes  through 
but  one  coil,  which  action  magnetizes  the  core.  When 
the  switch  is  closed,  however,  the  current  flows  through 
both  coils,  in  opposite  directions,  thereby  completely 
neutralizing  each  other. 


188  SOLENOIDS 

Another  method  is  to  connect  the  ends  of  each  layer 
to  common  terminals,  one  at  each  end  of  the  coil,  as  in 

Fig.  203,  p.  279. 

The  time  constants 
of  the  separate  circuits 
being  different,  owing 
to  the  varying  diame- 
ters of  the  layers  which 
makes  the  coefficient  of 
self-induction  less  and 

V V  V V V  V  V  \J  \J VW          the  resistance        tei. 

FIG.  158.  — Differential  Method.  .     ,,  ,  , 

in  the  outer  layers,  and 

vice  versa  in  the  inner  layers,  the  extra  current  flows 
out  at  different  times  for  different  coils. 

Copper  sleeves  are  also  sometimes  placed  over  the 
cores  of  electromagnets,  currents  being  set  up  in  the 
sleeves  at  the  time  of  breaking  the  circuit,  by  the  lines 
of  force  passing  through  them.  It  is  evident  that  there 
will  not  be  so  great  an  inductive  effect  in  the  winding 
when  much  of  the  energy  is  absorbed  by  the  copper 
sleeve. 

Tinfoil  is  also  interposed  between  the  layers  of  the 
winding,  for  the  same  purpose  as  above. 

Professor  Sylvanus  P.  Thompson,  who  made  a  com- 
parison test  of  the  following  methods,  found  that  the 
differential  method  was  the  best ;  the  multiple-wire 
winding,  tinfoil,  and  copper  sleeve  arrangements  follow- 
ing in  merit  in  the  order  given. 

The  multiple-wire  winding  referred  to  above  is,  in 
practice,  really  a  multiple-coil  winding.  This  is  treated 
in  Art.  163,  p.  277. 

The  spark  may  be  destroyed  by  a  blast  of  air  or  by 
means  of  a  magnet.  In  the  latter  case  the  field  of  the 


QUICK-ACTING  ELECTROMAGNETS  189 

magnet  repels  the  field  established  by  the  arc,  thus  de- 
stroying it. 

In  general,  it  may  be  stated  that  what  is  gained  in 
quickness  of  action  is  lost  in  current  consumption,  and 
vice  versa. 

91.    METHODS  OF  PREVENTING  STICKING 

If  the  armature  of  an  ordinary  horseshoe  electro- 
magnet be  placed  in  close  contact  with  the  pole  pieces 
before  the  magnet  is  energized,  it  may  be  easily  re- 
moved. However,  if  a  direct  current  be  passed  through 
the  windings  and  the  magnet  be  again  deenergized, 
the  armature  will  still  be  firmly  attracted  to  the  pole 
pieces.  This  is  due  to  the  residual  magnetization  of 
the  iron.  If,  however,  the  iron  or  ferric  portion  of  the 
magnetic  circuit  be  broken,  so  as  to  introduce  a  high 
reluctance,  the  greater  part  of  the  residual  charge  will 
disappear. 

As  this  feature  is  very  undesirable,  in  most  electro- 
magnets, non-magnetic  stops  are  usually  provided  which 
prevent  the  armature  from  actually  closing  the  magnetic 
circuit,  thereby  keeping  the  reluctance  so  high  that  the 
residual  magnetization  will  not  have  sufficient  effect 
upon  the  armature  as  to  interfere  with  the  proper  oper- 
ation. 

On  large  electromagnets,  in  particular,  brass  or  copper 
pins  are  forced  into  the  cores  to  prevent  "  sticking  "  of 
the  armature.  Where  these  pins  are  subject  to  a  heavy 
blow  from  the  armature,  they  should  have  sufficient 
area  to  withstand  the  blow  without  flattening. 

Another  method  is  to  place  a  strip  of  non-magnetic 
material  over  the  ends  of  the  cores.  This  is  sometimes 
made  in  the  form  of  a  cap.  On  small  electromagnets 


190  SOLENOIDS 

either  the  ends  of  the  cores  or  armature,  or  both,  are 
copper  plated,  the  thickness  of  the  copper  being  suffi- 
cient to  prevent  sticking.  The  copper  plating  also  has 
the  property  of  protecting  the  iron  from  oxidation. 

In  the  design  of  electromagnets,  the '  space  occupied 
by  the  non-magnetic  stops  must  be  taken  into  consider- 
ation. 


CHAPTER   XIV 
MATERIALS,   BOBBINS,  AND  TERMINALS 

92.   FERRIC   MATERIALS 

THE  materials  generally  used  in  the  construction  of 
the  cores  and  frame  are  iron  and  steel.  The  best  iron 
is  wrought  and  Swedish  iron.  Frames  may  be  made 
of  cast  iron  where  the  reluctance  of  the  air-gap  is  great, 
but  the  cores  should  always  be  made  of  the  best  grades 
of  iron  and  steel.  Cast  steel  is  largely  used  in  the  con- 
struction of  large  electromagnets,  and  tests  about  the 
same  as  wrought  iron  (see  p.  35). 

The  magnetic  properties  of  iron  and  steel  depend 
largely  upon  the  percentages  of  carbon  in  their  compo- 
sition, and  also  phosphorus,  sulphur,  manganese,  and 
silicon. 

Wrought  iron  contains  a  small  percentage  of  carbon, 
and  is  comparatively  soft,  maleable,  and  ductile.  '  It  has 
a  high  permeability,  but  has  the  disadvantage  of  being 
expensive,  unless  its  form  is  very  simple. 

Swedish  iron  has  about  the  same  permeability  as 
wrought  iron. 

Cast  steel  has  a  very  small  percentage  of  combined 
carbon  and  no  free  carbon,  and  the  best  grades  do  not 
contain  more  than  0.25  per  cent  of  carbon.  It  is 
cheaper  than  wrought  iron,  but  is  hard  to  obtain  on 
short  notice  and  in  small  quantities. 

Cast  iron  is  hard  and  quite  brittle,  and  contains  con- 

191 


192  SOLENOIDS 

siderable  carbon  in  the  free  state.  It  can  easily  be  ob- 
tained in  almost  any  desired  shape  at  a  low  cost. 

Irons  containing  more  than  0.8  per  cent  of  combined 
carbon  are  of  a  low  magnetic  permeability,  and  those 
having  less  than  0.3  per  cent  are  of  a  high  permeability. 
The  combined  carbon  should  be  kept  as  low  as  possible, 
while  the  free  carbon  may  vary  from  2  to  3  per  cent  with- 
out having  any  appreciable  effect  on  the  permeability. 

In  exact  work,  the  permeability  is  obtained  for  a 
sample  of  each  lot  of  iron  or  steel  used. 

93.   ANNEALING 

The  permeability  of  iron  is  increased  by  annealing. 
This  is  done  by  heating  the  iron  to  a  cherry-red,  and 
then  allowing  it  to  cool  gradually.  Special  charcoal 
ovens  are  provided  for  this  purpose. 

During  the  process  of  annealing  the  air  must  not 
come  into  contact  with  the  iron,  or  oxidation  will  result. 
Oxide  or  rapid  cooling  makes  the  iron  bad  as  an  electro- 
magnet core,  either  by  scale,  which  makes  the  magnet 
residual  on  the  outside,  or  by  hardening,  which  makes 
it  residual  on  the  inside,  and  in  the  latter  case  the  per- 
meability will  be  lower  than  as  though  the  iron  were 
soft. 

94.    HARD  RUBBER 

Hard  or  vulcanized  rubber  is  used  extensively  in  the 
manufacture  of  heads  or  washers  of  electromagnet  spools 
for  telegraph  and  various  other  types  of  electromagnetic 
apparatus. 

It  is  very  brittle  at  the  normal  temperature  of  the 
air,  but  becomes  soft  and  pliable  when  subjected  to 
slight  degrees  of  heat. 


MATERIALS,   BOBBINS,  AND  TERMINALS       193 

Its  insulating  qualities  are  excellent,  and  it  is  very 
useful  within  certain  limits  of  temperature.  Its  cost 
is  high  as  compared  with  fiber,  and  it  has  to  be  handled 
very  carefully  in  machining.  On  account  of  its  brittle- 
ness  it  must  be  softened  by  heating  before  forcing  on  to 
cores.  This  is  preferably  done  by  placing  it  in  warm 
water.  It  may  be  bent  into  almost  any  shape  when 
heated,  and  will  retain  its  form  after  becoming  cold. 

One  great  advantage  of  hard  rubber  is  that  it  may  be 
molded  or  cast  into  almost  any  desired  form.  It  also 
takes  a  very  high  polish,  and  is  therefore  very  much 
used  where  appearance  and  finish  are  desirable.  It  is 
furnished  in  both  the  sheet  and  rod. 

95.    VULCANIZED  FIBER 

The  commercial  fibers  are  of  three  kinds  and  are  sold 
under  the  following  trade  names :  Gray  Fiber,  Red 
Fiber,  and  Black  Fiber. 

The  cheaper,  and  consequently  the  more  common 
grades,  are  red  and  black.  Gray  fiber  is  the  best,  but 
is  somewhat  more  expensive. 

Fiber  serves  very  well  as  insulating  material  for  low 
voltages,  and  it  machines  quite  well,  though  not  so 
well  as  hard  rubber.  However,  it  is  not  so  brittle  as 
hard  rubber. 

Fiber  readily  absorbs  moisture  which  renders  it  prac- 
tically useless  for  high  voltages.  Nevertheless,  it  is 
used  extensively  for  heads  of  bobbins,  etc.,  and  makes 
an  excellent  body  upon  which  to  place  the  high-grade 
insulating  materials,  such  as  oiled  paper,  oiled  linen, 
mica,  Micanite,  etc. 

When  used  in  conjunction  with  some  high-grade 
insulating  material,  as  just  mentioned,  fiber  is  superior 


194  SOLENOIDS 

to  rubber,  and  does  not  soften  or  melt  like  rubber  at 
comparatively  low  temperatures,  but  it  is  liable  to  warp 
on  account  of  its  hygroscopic  properties. 

Fiber  is  especially  adaptable  for  the  making  of  bob- 
bins, as  the  tube  or  barrel  is  readily  made  to  any  size  by 
rolling  a  thin  sheet  of  it  around  a  mandrel,  cementing 
it  together  with  shellac  as  it  is  rolled. 

Small  heads  or  washers  are  usually  punched  from  the 
sheet.  On  account  of  its  toughness,  fiber  is  almost  ex- 
clusively used  in  making  heads  for  telephone  ringers, 
relays,  drops,  etc.,  as  the  heads  may  be  forced  on  with 
great  pressure  without  cracking,  thereby  insuring  firm 
and  solid  containing-walls  for  the  winding. 

All  grades  of  fiber  on  the  market  are  not  the  same, 
but  the  best  grades  show  no  signs  of  being  built  up  in 
layers,  and  will  not  readily  split  with  the  grain,  i.e. 
lengthwise. 

Vulcanized  fiber  is  furnished  in  both  the  sheet  and 
rod. 

96.    FORMS  OF  BOBBINS 

Bobbins  for  electromagnet  and  solenoid  windings  are 
made  of  various  materials  and  from  numerous  designs. 
The  natural  material  for  a  bobbin  of  this  character  is 
an  insulating  substance,  and  as  high-grade  insulating 
materials  are  more  expensive  than  materials  of  lesser 
insulating  properties,  the  insulating  material  in  the  bob- 
bin usually  depends  upon  the  voltage  between  the  wind- 
ing and  the  core,  or  the  outer  portion  of  the  bobbin. 
Thus  in  apparatus  where  low  voltages  are  to  be  used  the 
quality  of  the  insulating  material  used  in  the  bobbin 
need  not  be  very  high. 

Next  to  the  insulating  properties  of  the  bobbin,  the 


MATERIALS,   BOBBINS,   AND   TERMINALS       195 

strength  of  the  material  must  be  considered.  This  may 
again  be  subdivided  into  the  necessary  thickness  of  the 
insulating  material,  for  if  the  insulation  be  very  thick, 
for  a  limited  size  of  bobbin,  the  internal  dimensions  may 
be  too  small  for  the  necessary  winding. 

Another  feature  to  be  considered  is  the  finish  of  the 
bobbin  which,  while  often  of  little  consequence  where 
the  bobbin  is  concealed,  is  of  the  utmost  importance  in 
highly  finished  instruments  where  the  finish  of  the  bob- 
bin must  conform  with  the  rest  of  the  apparatus. 

In  this  case,  however,  the  actual  insulating  properties 
of  the  material  of  the  bobbin  may  or  may  not  be  of 
great  importance  owing  to  the  frequent  use  of  low 
voltage.  In  highly  finished  apparatus  the  bobbin  is 
usually  made  of  hard  rubber  which,  while  an  excellent 
insulator,  takes  a  very  high  polish. 

Bobbins  may  be  generally  classified  into  those  with 
iron  cores,  and  those  without  iron  cores.     Bobbins  with 
iron  cores  are  usually  made  as 
shown  in   Fig.   159.      In  this    _•-: 
type  the  heads  or  washers  are    ft- 
forced  on  to  the  core,  and  form    "-  - 
the  retaining  walls  of  the  wind- 
ing.  The  core  is  insulated  with     FlG  i59._Bobbm  with  iron 
paper  for  low  voltage,  or  with  Core, 

micanite  or  oiled  linen  for  high  voltages. 

For  high  voltages,  however,  special  precautions  must 
be  taken,  which  will  be  discussed  farther  on.  Bobbins 
of  the  type  shown  in  Fig.  159  are  sometimes  provided 
with  metal  washers.  In  such  cases  insulating  washers 
must  be  placed  upon  the  core  between  the  ends  of  the 
winding  and  the  metal  washers.  Here  the  thickness  of 
the  insulating  washers  depends  merely  upon  their  in- 


196  SOLENOIDS 

sulating  properties,  as  the  metal  washers  take  the 
mechanical  strain. 

Fiber  washers  may  be  forced  on  to  the  cores,  but  rub- 
ber will  crack  unless  great  care  is  exercised.  A  good 
way  to  prevent  the  washers  from  turning  on  the  core 
is  to  put  a  straight  knurl  on  each  end  of  the  core  before 
forcing  on  the  washers.  Rubber  washers  should  be 
dipped  in  hot  water,  and  then  forced  on  before  they 
become  brittle. 

Bobbins  without  iron  cores  may  also  be  classified  into 
those  having  metal  tubes  and  those  having  tubes  of 
insulating  materials.  In  the  former  t}^pe,  brass  is 
commonly  used  for  the  tube,  particularly  in  solenoids 
of  the  coil-and-plunger  type  where  there  will  be  con- 
siderable wear  on  the  inside  of  the  tube.  In  this  case 
the  tube  must  be  well  insulated  according  to  the  volt- 
age used.  Where  fiber  washers  are  used,  a  forced  fit 
is  usually  sufficient.  With  brass  washers,  however,  it 
is  best  to  thread  the  tube  and  washers  and  solder  them 
also.  All  soldering  should  be  done  without  the  use  of 
acid. 

Another  method,  and  particularly  where  a  thin  brass 
tube  and  brass  washers  are  to  be  used,  is  to  spin  up  the 
ends  of  the  tube.  Bobbins  of  this  type  with  thin  brass 
tubes  are  for  use  with  plunger  electromagnets,  etc., 
where  they  are  simply  placed  over  more  substantial 
brass  tubes  or  directly  upon  the  cores  themselves. 

Bobbins  with  heavy  brass  tubes  are  also  assembled  by 
turning  off  a  portion  at  the  ends  of  the  tube,  leaving  a 
shoulder  which  acts  as  a  distance-piece  between  the 
washers,  and  also  permits  the  ends  to  be  spun  up.  If  of 
metal,  the  washers  may  also  be  soldered. 

When  a  brass  tube  is  used  in   a   bobbin   for  alter- 


MATERIALS,   BOBBINS,   AND   TERMINALS       197 

nating-current  or  quick-acting  magnets,  the  tube  and 
washers  must  be  slotted.  Metal  bobbins  are  sometimes 
cast  in  one  piece. 

Bobbins  consisting  entirely  of  insulating  materials 
are  also  vulcanized  in  one  piece  with  such  materials  as 
hard  rubber  or  Vulcabeston.  They  are  also  turned  from 
the  solid  stock,  but  this  is  rather  an  expensive  method. 
The  usual  method  is  to  make  a  tube  of  paper,  rubber, 
micanite,  or  other  insulating  material,  and  cement  the 
washers  thereto  with  shellac  or  some  other  insulating 
compound. 

97.    TERMINALS 

The  terminals  of  electromagnetic  windings  may  be 
divided  into  two  classes  :  (#)  those  consisting  of  wires 
or  flexible  conductors,  and  (5)  devices  to  which  wires 
constituting  the  external  circuit  may  be  connected  by 
soldering  or  by  means  of  screws. 

Of  the  former  type,  the  most  natural  terminals  would 
be  the  ends  of  the  wires  constituting  the  winding. 
While  this  may  be  satisfactory  where  comparatively 
large  wires  are  used,  and  generally  where  there  is  not 
much  danger  of  the  wire  becoming  broken,  it  is  usually 
desirable  to  employ  flexible  stranded  terminals  of  cop- 
per, thoroughly  insulated,  whose  total  cross-section 
shall  be  at  least  as  great  as  the  cross-section  of  the  wire 
in  the  winding. 

In  the  case  of  multiple-coil  windings,  the  cross-section 
of  the  terminal  conductor  should  at  least  equal  the 
cross-section  of  the  wire  in  the  winding,  multiplied  by 
the  number  of  coils  constituting  the  total  winding. 

For  small  coils,  with  fine  wire,  a  terminal  conductor 
consisting  of  ten  stranded  copper  wires  insulated  with 


198  SOLENOIDS 

a  thin  coating  of  soft  rubber  and  covered  with  silk  is 
very  good.  The  wire  should  be  tinned  wherever  rubber 
is  used.  For  larger  coils,  ordinary  lamp  cord  is  excellent. 

The  inside  terminal  is  the  one  which  is  naturally 
the  more  important ;  for  if  this  should  become  broken,  it 
might  be  necessary  to  remove  the  entire  winding,  and 
rewind  the  coil. 

When  winding  on  an  ordinary  bobbin,  the  inside 
terminal  should  be  thoroughly  soldered  to  the  end  of 
the  wire  constituting  the  winding,  before  the  winding 
operation  is  begun,  wrapping  the  terminal  proper 
around  the  core  three  or  four  times  in  order  to  take 
the  strain  from  the  wire. 

The  joint  should  be  thoroughly  insulated  with  a  tough 
insulating  cloth  or  paper,  for,  unless  precautionary 
measures  be  taken,  the  coil  is  liable  to  "  break  down  " 
between  the  joint  and  the  succeeding  layer  of  wire. 

The  outside  terminal  should  be  connected  in  sub- 
stantially the  same  manner. 

When  it  is  necessary  to  bring  the  inner  terminal  to 
the  outside  of  the  coil,  strips  of  mica,  micanite,  or  oiled 
linen  should  be  placed  between  the  terminal  and  the 
rest  of  the  coil  to  prevent  a  "  break-down."  Thin  strips 
or  ribbons  of  copper  or  brass  may  be  used  where  the 
space  is  limited.  In  any  case  the  insulating  strip  should 
be  of  ample  width,  the  wider  the 
better. 

In  cases  where  binding-screws  are 

_  fastened  to  the  outside  of  the  coil, 

FIG.  160.  — Terminal    both   the   inner   and  outer  terminal 
Conductor.  wireg  shoul(}  be  thoroughly  insulated. 

For  ordinary  purposes,  where  the  coil  is  not  exposed 
to  oil  or  moisture,  the  type  of  terminal  conductor  shown 


MATERIALS,   BOBBINS,   AND   TERMINALS       199 

in  Fig.  160  may  be  used,  mica  or  other  suitable  insu- 
lating material  being  placed  between  the  connectors 
and  the  coil.  The  metal  strips,  to  which  the  connectors 
are  soldered,  should  be  just  long  enough  to  permit  of  a 
firm  mechanical  connection  with  the  coil,  by  wrapping 
tape  or  cord,  or  both  over  them. 

For  particular  work,  the  terminal  shown  in  Fig.  161  is 
recommended.  This  may  be  mounted  in  the  following 
manner :  First  place  a  sheet  of 
Micanite  about  14  mils  thick 
between  the  coil  and  the  ter-  » 
minal,  leaving  a  good  margin 

around  the  edges  to  prevent  FIG.  161.  — Terminal  Conductor 
any  "  jumping  "  of  the  current.  with  Water  Shield- 

The  terminals  may  be  firmly  held  to  the  coil  by  the  first 
wrapping  of  asbestos  tape,  stout  twine  being  first  em- 
ployed, which  is  removed  as  the  tape  is  applied. 

The  water  shield  is  applied  over  the  asbestos  tape  or 
paper  before  the   external  insulation   is   applied.     In 
soldering  the   terminals  on,  solder   having   a   melting 
point  of  400°  ¥  or  more  should  be  used.     Never  use  acid. 
Figures  162  to  164  are  suggestions  for  bringing  out 
flexible  terminals.     Figure  165  shows  the   method   of 
fastening  the  inside  and  outside  ter- 
minals by  means  of  cotton  or  asbestos 
tape.     In  each  case  the  end  of  the 
wire  is  passed  through  the  loop  which 
loop  is  <lr  a  w  n  t o g e t h e r  by  a  sharp  jerk 
on  the  protruding  end  of  the  tape. 
Terminals  for  small  electromagnets, 

FIG.  162.  — Method  of    sucn  as  are  used  On  telephone  Switch- 
bringing  out  Termi-    ,  ,  .   ,         „ 

nai  Wires.  board    apparatus,     consist    of    pins, 

clips,  etc. 


200 


SOLENOIDS 


A  good  method  of  connecting  the  inside  terminals  of 
a  pair  of  coils  011  a  horseshoe  electromagnet  is  to  cut  a 

piece     of     shel- 
lacked cotton 


FIG.  163.  —  Method  of  bringing  out  Terminal 
Wires. 


FIG.  164.  —  Method  of 
bringing  out  Termi- 
nal Wires. 


tubing  the  proper  length,  and  then  make  a  small  in- 
cision  midway   between   the    two    ends.      The   inside 


terminal  wires  are  then  passed  in  at 
opposite  ends  of  the  sleeve  ;  brought 
out  through  the  incision;  soldered, 
and  tucked  back  inside  of  the  sleeve. 
A  touch  with  a  brush  dipped  in 
shellac  seals  the  incision.  Rubber 
tubing  should  never  be  used  unless 

the  wires  are  tinned,  owing  to  the  corrosive  effect  of  the 

sulphur  in  the  rubber  on  the  copper  wire. 


Onrnrnnlhrn 


CCQQQQOOOOQ 

FIG.  165.— Methods  of 
tying  Inner  and 
Outer  Terminal 

Wires. 


CHAPTER   XV 


INSULATION  OF  COILS 

98.  GENERAL  INSULATION 

THE  complete  insulation  of  electromagnetic  windings 
consists  of  (a)  the  insulation  on  the  wire ;  (5)  the  in- 
ternal or  extra  insulation  placed  between  the  layers  of 
wire  in  the  winding,  and  impregnating  compounds  for 
improving  the  insulation  on  the  wire,  and  (<?)  the  ex- 
ternal or  insulation  placed  about  the  outside  of  the  wind- 
ing to  insulate  it  from  the  core,  frame,  etc.  The 
insulation  on  the  wire  is  treated  in  Chap.  XVII. 

99.  INTERNAL  INSULATION 

In  all  electromagnetic  windings  there  are  electrical 
stresses  between  adjacent  layers  and  turns.     This  pres- 
sure  varies   directly  with  the   total 
voltage  across   the  terminals   of  the 
winding,  and  the  length  of  the  wind- 
ing, and  inversely  with  the  number  of     FlG  1G(i  _  Sectional 
layers.     For  this  reason  it  is  desirable  Winding. 

to  keep  the  length  of  the  winding  as  small  as  possible. 
Where  it  is  necessary  to  use  a  long  winding,  it  is 
customary  to  form  the  winding  proper 
of  several  short  windings  connected 
in    series,    and    insulated    from    one 
FIG.  167.— insulation    another  at  the  ends,  as  in  Fig.  166. 
between  Layers.         For  particularly  heavy  duty,  it  is  also 
customary  to  place   paper,   mica,    or   insulating   linen 

201 


202  SOLENOIDS 

between  the  layers  of  the  winding.  The  paper  or  other 
insulating  material  should  project  a  short  distance  from 
each  end  of  the  winding,  as  in  Fig.  167.  This  will 
prevent  any  "jumping"  around  the  insulating  medium, 
from  layer  to  layer. 

Silk  and  cotton  covered  wire  coils  may  be  impreg- 
nated with  varnishes  and  other  compounds  specially 
prepared  for  the  purpose,  but  enameled  wire  is  better 
treated  by  the  "dry"  process,  i.e.  insulated  with  oiled 
linen  or  mica,  according  to  the  temperature  at  which  it 
is  to  be  operated. 

There  are  three  methods  of  treating  the  insulated 
wire  to  increase  the  dielectric  strength  and  to  make 
them  moisture-proof  ;  the  former  two,  described  below, 
being  practically  similar. 

In  one  of  these  methods  the  wound  coil  is  dipped  in 
an  insulating  compound  until  it  is  saturated  as  much  as 
possible  by  the  compound  or  varnish.  In  the  other 
similar  method,  the  wire  is  passed  through  a  bath  of 
insulating  substance,  in  liquid  form,  as  it  is  wound  in 
the  coil,  or  else  the  layers  are  painted  with  the  insulat- 
ing substance,  one  by  one,  as  they  are  wound  into  the 
coil. 

In  the  third  method,  the  coils  are  placed  in  a  vacuum 
chamber  and  the  air  pumped  out.  At  the  same  time 
the  moisture  is  expelled.  When  a  sufficient  degree  of 
vacuum  is  obtained,  a  melted  insulating  compound  is 
allowed  to  flow  into  the  vacuum  chamber,  at  the  pres- 
sure of  the  atmosphere.  As  no  air  is  allowed  to  re- 
turn to  the  chamber,  the  insulating  compound  fills  all 
the  interstices  between  the  turns. 

In  a  simple  vacuum  process,  the  coil  is  placed  di- 
rectly in  the  impregnating  compound,  and  the  air  is 


INSULATION  OF   COILS  203 

then  pumped  out.  The  latter  method  is  not  considered 
so  desirable  as  the  former,  however,  as  the  moisture  is 
not  so'  readily  expelled  in  the  latter  method. 

Insulating  varnish  may  also  be  used  in  the  vacuum 
drying  and  substituting  process,  the  coil  being  thor- 
oughly baked  afterwards. 

In  coils  designed  for  use  on  alternating  currents,  it 
is  customary  to  place  mica,  oiled  linen,  or  paper  between 
the  layers,  and  treat  it  with  some  insulating  and  im- 
pregnating compound  besides. 

The  material  for  the  internal  insulation  of  the  coil 
should  be  oil  and  moisture  proof,  chemically  inert,  and 
a  good  conductor  of  heat.  Moreover,  it  should  be 
mechanically  strong,  so  as  to  cement  the  coil  in  one 
solid  mass,  so  that  the  wire  cannot  vibrate  and  thus 
injure  its  insulation.  It  should  also  be  unaffected  by 
the  heat  at  the  ordinary  operating  temperature. 

Solid  and  paraffin  compounds  tend  to  soften  under 
the  influence  of  heat.  Paraffin  compounds,  while  non- 
hygroscopic,  are  poor  mechanically,  and  are  soluble  in 
mineral  oils.  For  these  reasons,  oil  varnishes  are  the 
more  preferable.  A  good  varnish  should  not  contain 
volatile  thinners,  as  these  thinners  are  driven  off  when 
the  coil  is  baked,  leaving  the  inside  of  the  coil  more  or 
less  porous. 

The  internal  insulation  of  asbestos-covered  *  wire 
windings  may  be  affected  by  dipping  the  wound  coil, 
while  hot,  in  fairly  thick  Armalac,  density  38°  B., 
allowing  the  coil  to  drain  a  few  minutes  after  each  dip- 
ping. The  coil  is  preferably  heated  by  suspending  it 
for  a  short  time  in  an  oven,  the  temperature  being 
raised  to  about  200°  F. 

*  D.  &  W.  Fuse  Co. 


204  SOLENOIDS 

100.    EXTERNAL  INSULATION 

The  external  insulation  consists,  in  the  ordinary  form 
of  winding  on  a  bobbin,  of  the  insulating  sleeve  over 
the  core,  the  insulating  washers  at  the  ends,  and  the 
wrapping  around  the  outside  of  the  coil.  These  are 
usually  paper,  fiber,  hard  rubber,  oiled  linen,  mica,  etc., 
depending  upon  the  voltage,  and  the  uses  to  which  they 
are  to  be  applied. 

In  many  cases  the  bobbin  itself  consists  of  insulating 
material,  in  which  case  only  the  outer  wrapping  need 
be  considered. 

In  any  type  of  bobbin,  whether  of  brass  or  of  fiber  or 
other  material  of  low  insulating  qualities,  the  following 
precautions  should  be  taken  to  insulate  the  bobbin  for 
a  high  voltage.  Around  the  tube  place  several  wraps 
of  oiled  linen  or  similar  material,  the  number  of  wraps 
to  be  at  least  twice  those  necessary  to  resist  the  voltage, 
as  specified  in  the  table  on  p.  325.  The  reason  why 
twice  the  thickness  should  be  used  will  be  explained 
presently. 

Lay  out  3.1416  times  the  diameter  of  the  tube  for 
the  first  wrap,  and  divide  this  into  such  a  number  of 
parts  that  the  width  of  each  fringe  shall  be  at  least 
J  inch  (this  may  be  less  when  smaller  diameters  require 

it). 

For  the  next  wrap,  consider  the  diameter  of  the  tube 
plus  the  first  wrap  as  the  new  diameter,  and  proceed  as 
before,  this  time  having  the  same  number  of  segments 
as  in  the  first  layer.  This  may  be  carried  out  as  far  as 
desired. 

If  these  directions  are  carefully  followed,  the  fringed 
ends  will  lap,  as  in  Fig.  168.  When  the  linen  is  in 


INSULATION   OF   COILS 


205 


place  in  the  bobbin,  the  fringed  ends  will,  of  course, 
rest  radially  against  the  washers. 

A  sufficient  number  of  oiled  linen  or  mica  washers 
should  now  be  placed  over  the  fringed  ends  to  prevent 


FIG.  168. —  Method  of  mounting  Fringed  Insulation. 

any  jumping  to  the  metal  washers,  and  two  pressboard 
washers,  one  at  each  end,  should  be  put  on  to  take  the 
wear  of  the  winding,  care  being  taken  to  have  the  slits 
or  cuts  in  the  linen  washers  at  least  90°  apart,  so  that 
there  can  be  no  leakage  at  these  points.  It  is  better  to 
assemble  the  linen  washers  before  the  brass  washers,  as 
then  the  linen  will  not  have  to  cut.  The  linen  washers 


206  SOLENOIDS 

should  be  placed  over  the  wrapping  of  linen   on   the 
tube,  with  the  fringe  between  the  metal   washer   and 

Ijrj  the  linen  washer.  The 
Hk  bobbin  will  then  ap- 
&  QJE  Pear'  as  in  Fi£'  169' 


The  corners  a-a  may 

FIG.  169. -Insulation  of  Bobbins.  ^Q   painted    with    var- 

nish,  and  the  whole  thoroughly  baked.  This  makes  a 
highly  insulated  bobbin.  By  this  method,  brass  bobbins 
may  be  used  and,  therefore,  much  space  saved.  The 
bobbin  may  also  be  insulated  with  micanite,  as  in 
Fig.  170. 

After  the  coil  is 
wound  and  treated, 
it  may  be  wrapped 
with  oiled  linen  or 


Canvas     in     sheet     Or  FIG.  170.  — Insulation  of  Bobbins. 

tape  form.  Over  this  may  be  placed  cord  or  pressboard, 
for  protection.  The  whole  should  then  be  dipped  in 
insulating  varnish  and  thoroughly  baked,  this  operation 
being  repeated,  for  good  results. 

Instead  of  first  insulating  the  bobbin  and  then  wind- 
ing on  the  wire,  the  coil  is  often  wound  and  insulated 
separately,  before  mounting  it  on  the  core.  While  this 
type  is  employed  on  solenoids,  lifting  and  plunger 
electromagnets,  in  which  case  it  is  usually  circular  in 
form,  it  is  particularly  used  for  the  field  magnets  of 
motors  and  generators.  This  type  is  known  as  a 
"  former  "  winding,  since  it  is  wound  on  a  collapsible 
form. 

For  the  external  insulation  of  this  type  of  winding, 
the  treated  coil  may  be  covered  successively  with  mica 
cloth,  leatheroid,  and  linen  tape,  the  whole  being  dipped 


INSULATION  OF  COILS  207 

in  varnish  which  is  oil  and  moisture  proof,  and  then 
thoroughly  baked. 

For  asbestos-covered  wires,  the  following  *  is  recom- 
mended: 

Mix  thoroughly,  while  dry,  equal  parts  of  red  oxide 
of  iron  and  powdered  asbestos,  or  asbestos  meals,  as  it  is 
sometimes  called,  then  stir  in  sufficient  Armalac  or 
other  approved  insulating  compound  to  make  up  a 
thick  putty  or  paste.  This  paste  can  be  readily  applied 
to  the  surface  of  the  coil  with  a  blunt  knife,  and  should 
be  so  applied  as  to  leave  the  coil  quite  smooth  and  free 
from  all  air  spaces.  The  object  of  this  material  is  to 
prevent  the  possibility  of  air  pockets  which  interfere 
with  the  radiation  of  heat,  and  at  the  same  time  to 
improve  the  insulation  of  the  coil  and  increase  its  water 
resisting  properties. 

As  this  paste,  or  Dobe,  is  applied,  a  first  wrapping  of 
pure  asbestos,  double-selvage  edge,  woven  tape,  f  inch 
X  0.02  inch  thick,  should  be  wrapped  around  the  coil. 
The  best  results  are  secured  by  winding  this  into  the 
Dobe  as  the  latter  is  applied,  which  in  a  measure 
partially  impregnates  the  tape  and  fills  up  the  spaces 
between  the  wrappings. 

The  coil  should  now  be  baked  for  about  an  hour,  with 
the  object  of  partially  drying  the  Dobe  and  at  the  same 
time  driving  off  any  moisture  which  the  tape  might 
contain.  The  temperature  should  be  raised  slowly  to 
about  200°  F.,  when  the  coil  should  be  taken  out  and 
dipped  in  Armalac  or  other  approved  insulating  com- 
pound, to  thoroughly  saturate  the  tape  while  hot.  It 
should  then  be  baked  for  a  period  of  about  four  hours,  the 
temperature  being  raised  by  degrees  to  at  least  400°  F. 
*  D.  &.  W.  Fuse  Co. 


208  SOLENOIDS 

It  should  then  be  removed  from  the  baking  oven  and 
allowed  to  cool  off  until  only  slightly  warm,  when.it 
should  be  coated  with  some  sort  of  adhesive  varnish 
such  as  shellac,  or  preferably,  Walpole  gum,  which  has 
been  found  very  satisfactory,  to  bring  about  a  close 
adhesion  between  this  and  the  paper  covering  which  is 
next  put  on. 

The  paper  jacket  consists  of  a  single  thickness  of  0.03- 
inch  asbestos  paper,  which  is  applied  in  a  dampened  con- 
dition in  order  to  facilitate  forming  it  closely  about  the  coil. 
It  is  preferably  first  cut  into  shapes  which  will  readily 
lend  themselves  to  this  formation,  the  edges  being  se- 
cured by  any  suitable  water  paste,  care  being  taken  to 
employ  only  as  little  of  this  paste  as  possible.  Over 
this  another  layer  of  asbestos  tape  is  wound. 

The  coil  should  now  be  thoroughly  dried  out  and 
baked  for  at  least  two  hours,  the  temperature  being  raised 
slowly  to  not  less  than  400°  F.  While  the  coil  is  at 
its  maximum  temperature,  it  should  be  taken  from  the 
oven  and  immersed  for  45  minutes  in  Delta  compound, 
which  has  previously  been  heated  to  at  least  350°  F. 
The  coil  may  be  suspended  by  means  of  asbestos  tape, 
as  it  will  not  burn  through. 

After  removing  the  coil  from  the  compound,  wipe  off 
the  surplus  and  bake  for  three  hours  at  350°  F. 
This  tends  to  set  the  compound  thoroughly  into  the 
wrapping  and  to  drive  off  the  volatile  matter  which  will 
prevent  the  water-proofing  material  from  softening. 
While  the  coil  is  still  hot,  it  should  be  finished  by 
immersing  in  any  suitable  baking  Japan,  preferably  one 
which  will  remain  in  a  flexible  condition  after  it  has 
hardened.  Two  or  three  coats  will  add  much  to  the 
life  of  the  coil. 


INSULATION   OF   COILS  209 

Coils  insulated  in  this  manner  have  been  put  to  the 
most  severe  service  imaginable  without  injury,  although 
at  times  they  have  been  completely  immersed  in  boiling 
water  for  long  periods. 

Coils  may  also  be  thoroughly  dried  and  baked  by 
passing  a  current  of  electricity  through  them.  In  this 
case  an  ammeter  and  rheostat  should  be  included  in  the 
circuit. 


CHAPTER    XVI 
MAGNET  WIRE 
101.    MATERIAL 

THE  ideal  electrical  conducting  material  would  be 
one  which  would  offer  no  resistance  whatever  to  the 
electromotive  force.  In  practice,  however,  the  ideal  is 
not  attainable.  It  is,  therefore,  natural  to  seek  the  best 
conducting  material  as  well  as  the  most  economical, 
using  that  which  is  most  practicable.  This  condition 
is  met  with  copper  wire. 

Since,  in  magnet  windings,  it  is  desirable  to  obtain 
the  maximum  number  of  turns,  with  a  minimum  resist- 
ance in  a  given  winding  space,  it  is  readily  seen  that, 
while  aluminum  may  be  used  to  advantage  in  trans- 
mission lines,  from  an  economical  standpoint,  its  use  in 
magnet  windings  is  prohibitive,  owing  to  its  greater 
Specific  Resistance  or  Resistivity. 

102.   SPECIFIC  RESISTANCE 

The  Specific  Resistance  of  a  material  is  the  resistance 
in  ohm  at  0°  C.  of  a  wire  one  centimeter  long  and 
one  square  centimeter  in  cross-section. 

The  specific  resistance  of  pure  annealed  copper  is 
1.584  x  10~6,  and  for  hard-drawn  copper,  1.619  x  10~6. 
The  specific  resistance  of  copper  varies  with  its  tempera- 
ture. The  ratio  of  change  in  resistance  to  change  in 
temperature  is  called  the  Temperature  Coefficient. 

The  chemical  purity  and  mechanical  treatment  of 
copper  have  marked  effects  upon  its  properties. 

210 


MAGNET   WIRE  211 

103.    MANUFACTURE 

In  the  manufacture  of  copper  wire,  ingots  of  com- 
mercially pure  copper  are  rolled  into  rods,  and  the  wire 
is  then  drawn  from  these  rods.  Rolling  improves  the 
structure  of  copper  wires.  Hence,  the  smaller  wires 
may  be  considered  of  better  quality  than  the  larger 
sizes. 

Commercial  copper  wires  are  usually  round,  although 
they  may  be  obtained  with  square  and  rectangular 
cross-sections.  In  this  book,  round  wire  will  be  assumed 
unless  otherwise  specified.  In  all  cases  a  wire  should 
be  of  uniform  cross-section  throughout  its  entire  length. 

104.    STRANDED  CONDUCTOR 

Where  a  conductor  of  large  cross-section  is  required, 
and  especially  if  it  is  to  be  wound  upon  a  small  core,  it 
may  be  stranded;  i.e.  it  may  consist  of  enough  smaller 
wires  to  make  the  total  cross-section  equal  to  the  cross- 
section  of  the  large  conductor.  This  makes  a  very 
flexible  conductor.  The  space  factor  of  a  stranded 
conductor  is  much  larger  than  that  for  a  solid  con- 
ductor. For  equal  diameters,  cables  or  strands  have 
a  conducting  area  of  from  20  to  25  per  cent  less  than  a 
solid  circular  conductor. 

A  table  showing  the  approximate  equivalent  cross- 
sections  of  wires  will  be  found  on  p.  307. 

105.   NOTATION  USED   IN  CALCULATIONS  FOR  BARE 

WIRES 

In  this  book  the  following  symbols  are  used  in  con- 
nection with  bare-wire  calculations: 


212  SOLENOIDS 

WB  =  total  weight, 
Wi  =  weight  per  unit  length, 
Wc  =  weight  per  unit  volume, 
lw  =  length  of  wire, 
p(  =  resistance  per  unit  length, 
pw  =  resistance  per  unit  weight, 
pv  =  resistance  per  unit  volume, 
R  =  total  resistance, 
d  =  diameter  of  wire, 
:  Wc—  8.89  grams  per  cubic  centimeter, 
=  0.321  pound  per  cubic  inch. 

106.    WEIGHT  OF  COPPER  WIRE 
Since  the  weight  per  unit  volume,  for  copper,  accord- 
ing to  Matthiessen's  standard,  is  8.89  grams  per  cubic 
centimeter,  or  0.321    pound  per  cubic   inch,  the  total 
weight  of  any  solid  mass  of  copper  would  be 

WB=WeV,  (162) 

wherein  V=  volume  of  copper. 

Since,  in  practice,  round  wire  is  used, 

TFs=  0.7854  WeV,  (163) 

neglecting  imbedding  of  the  wires,  etc.,  which  is  dis- 
cussed in  Chap.  XVIII. 

107.    RELATIONS   BETWEEN   WEIGHT,   LENGTH,    AND 
RESISTANCE 

Weight  may  be  found  from  length  or  resistance. 


B  =  1WW{    (164),        =.(165),       Wt  =  (166) 

Pw  lw 

Length  may  be  found  from  weight  or  resistance. 


MAGNET   WIRE  213 

=A  (168) 

Resistance  may  be  found  from  weight  or  length. 

R^P.W,,     (169),  =l,,p,.  (170) 

ft=£     (171),  ft.  =  -|-.  (172) 

C  ^£ 

108.    THE  DETERMINATION  OF  COPPER  CONSTANTS 

Specific  gravity  of  copper  .         8.89 

1  foot 0.3048028  meter 

1  meter 3.28083  feet 

1  inch       .         .         .         .         .         2.54  centimeters 

1  pound 453.59256  grams 

1  gram 0.0022046  pound 

1  square  centimeter  .         .  1.55  square  inches 

1  gram      .         .       1  cubic  centimeter  of  water  at  4°  C. 
1  gram   of    copper  =  1  -f-  8.89  =  0.112486    cubic  centi- 
meters. 

Therefore,  a  wire  100  centimeters  long,  containing 
0.112486  cubic  centimeter  of  copper,  will  be  0.00112486 
square  centimeter  or  0.000174353  square  inch  in  cross- 
section,  and  this  has  been  found  to  have  a  resistance  of 
0.141729  International  ohm  at  0°  C.  Hence,  a  wire 
one  foot  long  and  0.000174353  square  inch  in  cross- 
section  has  a  resistance  of  0.0431991  International  ohm 
at  0°  C.  From  this  it  follows  that  a  wire  0.001  inch 
(1  mil)  in  diameter  (0.0000000785398  square  inch,  or  1 
circular  mil,  in  cross-section)  will  have  a  resistance  of 
9.58992  International  ohms  per  foot  at  0°  C.,or  10.3541 
ohms  per  foot  at  20°  C.  or  68°  F. 


214  SOLENOIDS 

Therefore,  in  English  units, 

PF  =  30,269  x  10-*  <P,  (173) 


(174) 

FP  =  33,036  x  10~6  d'\  (175) 

-F0  =  96,585  d2,  (176) 

OP  =  342x1  0-8d-4,  (177) 

0P  =  103,541  x  10~10  d~\  (178) 

Oj  =  86,284  x  10-11  d~*  ;  (179) 

wherein       Pf=  pounds  per  foot, 
P0  =  pounds  per  ohm, 
FP  —  feet  per  pound, 
F0  =  feet  per  ohm, 
Op  =  ohms  per  pound, 
0F  =  ohms  per  foot, 
Of  =  ohms  per  inch, 
d  =  diameter  of  wire  in  inch. 

In  metric  units, 

JTJ/=698x  lO-5^2,  (180) 

K0=  3186x10-4  d\  (181) 

MK  =  1433  x  10-1  d-a,  (182) 

(183) 

4,  (184) 

2,  (185) 

Ocm  .=  2192  x  10-8  d~*  ;  (186) 

wherein       KM=  kilograms  per  meter, 
K0  =  kilograms  per  ohm, 


MAGNET  WIRE  215 

MK  —  meters  per  kilogram, 
M0  =  meters  per  ohm, 

0K  =  kilograms  per  ohm, 

0M=  ohms  per  meter, 
Ocm  =  ohms  per  centimeter, 
d  =  diameter  of  wire  in  millimeters. 

109.    AMERICAN  WIRE  GAUGE  (B.  &  S.) 

This  is  the  standard  wire  gauge  in  use  in  the  United 
States.  It  is  based  on  the  geometrical  series  in  which 
No.  0000  is  0.46  inch  diameter,  and  No.  36  is  0.005  inch 
diameter. 

Let  n  =  the  number  representing  the  size  of  wire, 
d=  diameter  of  the  wire  in  inch. 

Then  log  d=  1.5116973  -0.0503535  n,  (187) 


and  =  -og  (188) 

0.0503535 

n  may  represent  half,  quarter,  or  decimal  sizes. 

If  d  represent  the  diameter  of  the  wire  in  millimeters, 

then  log  d  =  0.9165312  -  0.0503535  n,          (189) 

d  _  0.9165312-  log  d 

0.0503535  (190) 

The  ratio  of  diameters  is  2.0050  for  every  six  sizes, 
while  the  cross-sections,  and  consequently  the  conduc- 
tances, vary  in  the  ratio  of  nearly  2  for  every  three  sizes. 

110.    WIRE  TABLES 

Wire  tables  showing  the  diameters,  sectional  areas,  and 
the  relations  between  weight,  length,  and  resistance,  for 
the  various  gauge  numbers,  will  be  found  on  pp.  305 
and  306. 


216  SOLENOIDS 

The  following  "Explanation  of  Table"  refers  to  the 
table  on  p.  305,  and  is  copied  from  the  Supplement  to 
Transactions  of  American  Institute  of  Electrical  Engi- 
neers. * 

"  The  data  from  which  this  table  has  been  computed 
are  as  follows:  Matthiessen's  standard  resistivity, 
Matthiessen's  temperature  coefficients,  specific  gravity 
of  copper  ==  8.89.  Resistance  in  terms  of  the  interna- 
tional ohm. 

"Matthiessen's  standard  1  metre-gramme  of  hard 
drawn  copper  =  0.1469  B.  A.  U.  @  0°  C.  Ratio  of  re- 
sistivity hard  to  soft  copper  1.0226. 

"Matthiessen's  standard  1  metre-gramme  of  soft 
drawn  copper  =  0.14365  B.  A.  U.@0°C.  OneB.  A.U. 
=  0.9866  international  ohms. 

"  Matthiessen's  standard  1  metre-gramme  soft  drawn 
copper  =  0.141729  international  ohm  @  0°  C. 

"Temperature  coefficients  of  resistance  for  20°  C., 
50°  C.,  and  80°  C.,  1.07968,1.20625,  and  1.33681 
respectively.  1  foot  =  0.3048028  metre,  1  pound  = 
453.59256  grammes. 

"  Although  the  entries  in  the  table  are  carried  to  the 
fourth  significant  digit,  the  computations  have  been 
carried  to  at  least  five  figures.  The  last  digit  is  there- 
fore correct  to  within  half  a  unit,  representing  an  arith- 
metical degree  of  accuracy  of  at  least  one  part  in  two 
thousand.  The  diameters  of  the  B.  &  S.  or  A.  W.  G. 
wires  are  obtained  from  the  geometrical  series  in  which 
No.  0000  =  0.4600  inch,  and  No.  36  =  0.005  inch,  the 
nearest  fourth  significant  digit  being  retained  in  the 
areas  and  diameters  so  deduced. 

"It  is  to  be  observed  that  while  Matthiessen's  standard 
*  October,  1893. 


MAGNET   WIRE  217 

of  resistivity  may  be  permanently  recognized,  the  tem- 
perature coefficient  of  its  variation  which  he  introduced, 
and  which  is  here  used,  may  in  future  undergo  slight 
revision. 


F.  B.  Crocker, 

G.  A.  Hamilton, 
W.  E.  Geyer, 

A.  E.  Kennely,  Chairman, 


Committee  on  ;  Units 
and  Standards.'" 


The  metric  wire  table  on  p.  306  was  calculated  by  the 
author  by  means  of  6-place  logarithms,  and  carefully 
checked  with  a  slide-rule,  the  computations  being  carried 
to  the  fourth  significant  digit.  The  last  digit  is  there- 
fore correct  to  within  half  a  unit. 

111.   SQUARE  OR  RECTANGULAR  WIRE  OR  RIBBON 

Copper  wire  is  sometimes  made  square,  but  wires  of 
this  class  are  usually  rectangular  in  cross-section. 
These  latter  wires  are  commonly  called  ribbons,  and  are 
rolled  from  the  standard  B.  &  S.  round  wires. 

In  order  to  calculate  one  dimension,  the  other  must 
first  be  assumed. 

If  we  let  ab  =  cross-sectional  area  of  ribbon, 

then  «= 


and  ,=  0.7854^  (192) 


and  the  diameter  of  a  round  wire,  to  have  the  same 
cross-  section  as  the  ribbon,  will  be 

d  =  1.128Vo6.  (193) 


218 


SOLENOIDS 


In  some  cases  the  ratio  of  thickness  to  width  of  cop- 
per ribbon  is  given  instead  of  one  of  the  dimensions. 
Then  if  Aw  represents  the  cross-sectional  area  of  the 
conductor,  and  p  and  q  are  the  ratios,  and  a  and  b  repre- 
sent the  dimensions  of  the  strip,  a  :  b  —  p  :  q,  whence 


and 
Now 
Therefore, 


p 

ab=A,n. 


P 


(197),        = 


Then     a=.     (199), 


p 


(194) 

(195) 
(196) 

(198) 

(200) 


112.    RESISTANCE  WIRES 


In  the  following  table*  are  several  resistance  wires, 
with  their  relative  resistances  as  compared  with  copper. 


RESISTANCE 

TEMPERATURE 

TEMPERATURE 

MATERIAL 

FEE  MIL 
FOOT 

COEFFICIENT 
PER  DEQ.  F. 

COEFFICIENT 

PER    DEG.    C. 

COMPARATIVE 
RESISTANCE 

Copper      .     . 

10.3541  @  68°  F. 

0.00215 

0.00388 

1 

Ferro-nickel 

170  @  75°  F. 

0.00115 

0.00207 

17 

Manganm     . 

248.8 

0.00001 

0.000018 

24 

Advance  .     . 

294 

Practi- 

cally  nil 

28 

S.  B.    .     .     . 

336 

0.000032 

0.000058 

32 

Climax     .     . 

525 

0.0003 

0.00054 

50 

Nichrome 

570 

0.00024 

0.000243 

55 

From  data  furnished  by  Driver-Harris  Wire  Co. 


MAGNET  WIRE  219 

For  tables  giving  further  information,  see  pp.  317-321. 

Under  similar  conditions,  the  carrying  capacity  of 
two  wires  of  equal  diameter,  but  of  different  materials, 
varies  inversely  as  the  square  root  of  their  specific  re- 
sistances. 


CHAPTER   XVII 

INSULATED  WIRES 

113.  THE  INSULATION 

IN  electromagnetic  windings  it  is  necessary  to  insu- 
late the  turns  from  one  another,  and  various  means  are 
adopted  for  this  purpose.  While,  in  some  windings, 
bare  wire  is  coiled  with  a  strand  of  silk  or  cotton,  or 
merely  an  air  space,  between  adjacent  turns,  and  with 
paper  between  adjacent  layers,  the  usual  method  is  to 
first  cover  the  wire  with  some  insulating  material  before 
coiling  it  into  the  winding. 

This  insulation  is  a  very  important  factor  in  electro- 
magnetic windings.  An  ideally  perfect  insulation  for 
this  purpose  should  be  vanishingly  thin,  and  have  a  high 
dielectric  strength.  Mechanically  it  should  be  hard, 
tough,  and  elastic.  The  thickness  of  the  insulation 
should  be  uniform.  It  should  be  non-hygroscopic, 
chemically  inert,  and  unaffected  by  high  temperatures. 

While  there  is,  at  the  present,  no  material  which 
fully  satisfies  all  of  the  above  requirements,  there  are, 
nevertheless,  several  materials  in  use  which  are  well 
adapted  for  this  purpose. 

114.   INSULATING  MATERIALS  IN  COMMON  USE 

Cotton  is  used  to  a  large  extent  on  the  larger  sizes  of 
wires  where  the  ratio  of  insulation  to  copper  will  not  be 
great.  It  is  well  adapted  as  a  spacer,  although  it  is  very 

220 


INSULATED   WIRES  221 

hygroscopic,  and  dielectrically  and  mechanically  weak. 
It  is  not  adapted  for  temperatures  over  100°  C. 

Silk  is  extensively  used  on  the  finer  sizes  of  wire, 
owing  to  its  small  factor  of  space  consumption,  although 
the  cost  is  much  greater  than  that  of  cotton. 

Asbestos,  while  having  approximately  the  same  char- 
acteristics as  cotton  mechanically,  hygroscopically,  and 
as  an  insulator,  has  the  desirable  ability  to  withstand 
high  temperatures.  It  is,  however,  expensive  and  occu- 
pies somewhat  more  space  than  the  cotton  insulation. 

Enameled  wire  is  quite  rapidly  superseding  cotton 
and  silk  covered  wires,  owing  to  its  small  space  factor, 
high  dielectric  strength,  and  its  ability  to  withstand 
high  temperatures.  It  is  non -hygroscopic. 

The  enamel  has  a  tendency  to  become  brittle,  and  to 
crack  when  large  enameled  wires  are  sharply  bent. 
This,  however,  has  been  largely  overcome  by  some  man- 
ufacturers. 

Paper  is  also  sometimes  used  to  insulate  wires. 

115.  METHODS  OF  INSULATING  WIRES 
Wire  is  insulated  with  cotton,  silk,  and  asbestos,  by 
covering  the  wire  with  threads  of  the  insulating  ma- 
terial. This  is  done  by  automatic  machinery  in  a  very 
economical  manner.  Paper  strips  are  also  wrapped 
around  the  wire  in  a  similar  manner,  the  paper  being 
held  in  place  by  a  suitable  varnish  or  paste,  which  will 
cause  it  to  adhere  tightly  to  the  wire. 

Wire  is  insulated  with  enamel  by  passing  it  through 
a  long  vessel  containing  enamel  in  a  liquid  state,  then 
passing  it  upward  and  then  downward  through  a  space 
in  which  the  temperature  is  automatically  maintained 
constant  at  about  300°  F.  by  means  of  gas  flames  con- 


222  SOLENOIDS 

trolled  by  thermostats.  The  speed  of  travel  of  the 
wire,  the  length  within  the  heated  space  and  the  tem- 
perature are  so  adjusted  according  to  the  thickness  of 
enamel  that  each  particle  is  thoroughly  baked  when  it 
passes  downward,  and  the  wire  is  dipped  into  a  second 
enameling  vessel,  and  so  on  until  three  coats  of  enamel 
have  been  placed  on  the  wire.  The  fourth  coat,  which 
is  an  exceedingly  thin  one,  is  applied  in  the  same  manner 
and  similarly  dried,  and  gives  an  excellent  finish  to  the 
product. 

This  operation  is  accomplished  by  machines,  each  of 
which  usually  handles  twelve  wires  simultaneously. 

116.    TEMPERATURE-RESISTING  QUALITIES  OF 
INSULATION 

The  tests*  of  magnet  wire  described  below  were  un- 
dertaken as  a  result  of  considerable  trouble  from  the 
field  coils  of  motors  breaking  down,  due  to  exposure  to 
high  temperatures.  The  motors  w^ere  mostly  on  furnace 
cranes  handling  molten  metal,  and  the  temperature  of 
the  cases  frequently  reached  360°  to  400°  F. 

Referring  to  Fig.  171,  curve  A  shows  the  results  of  a 
test  on  No.  16  B.  &  S.  double-cotton-covered  magnet 
wire  of  0.060  inch  outside  diameter.  The  covering  at 
280°  F.  showed  discoloration ;  at  370°  F.  the  covering 
was  smoking  badly,  and  at  472°  the  wire  was  completely 
bare.  This  wire  showed  the  highest  insulation  resist- 
ance at  the  start,  but  fell  down  after  passing  370°. 

Curve  B  refers  to  a  test  on  No.  16  B.  &  S.  asbestos 
and  single-cotton-covered  wire.  At  340°  a  slight  smoke 
showed  up ;  at  372°  discoloration  of  cotton  took  place ; 
at  460°  the  cotton  burned,  and  at  506°  cotton  was  gone. 

*  C.  H.  Barrett,  Electrical  World  and  Engineer,  Dec.  23,  1905. 


INSULATED  WIRES 


223 


From  506°  up  to  720°,  which  was  the  limit  of  the  ther- 
mometer in  use,  the  asbestos  held  good  and  showed  an 
insulation  resistance  of  480  megohms  at  close,  against 
11  megohms  at  start.  The  asbestos,  however,  would 
not  stand  very  rough  handling,  though  considering 
the  temperature  it  was  in  pretty  fair  shape.  The 
outside  diameter  over  insulation  of  this  wire  was 
0.068  inch. 

3    6    9    12  15  18  21  24  27  30  33  36  39  42  45  48  51  54 


you 

Th 

•ee 

ml 

nut 

er^ 

ad 

ng 

k 

E 

mon 
mit 

eter 

bW 

700 
600 

/ 

/j 

000 

500 

0 

1 

/r 

i 

.--'• 
.ton 

gont 

500 

PH 

C( 

tton 

W 

ned 

>«W 

' 

^Xj 

o> 

A/. 

Cot 

ton 

jurn 

"g 

400 

9. 

<r'^f/ 

400 

c;- 

T 

Cot 

on  ; 

Ml 

mzx 

^; 

VJS'fri' 

colo 

ed 

^ 

^ 

Slig 

ht  s 

nok 

300 

o 
En 

/ 

^ 

/ 

n^ 

he 

16 

J.S. 
^S 

Dou 
Asb< 

hie 

StOfl 

:ottr 

&s 

nCc 

inrl 

vert 

To 

d. 
ton 

red 

•200 

D| 

coli 

CPj^ 

' 

C= 

3.S. 

Fireproo 

1  Asoeste 

sCo 

vere 

1. 

200 

( 

*'/ 

' 

Ins 

Res 

stan 

:eoJ 

A. 

t  start  • 

-  20 

Me 

tohJ 

s. 

/s 

tt 

(f 

B 

»    *!•     = 

=  11 

100 

^ 

f 

" 

•• 

•  • 

C 

.     A      -. 

:       7 

100 

,  -H 

M 

j 

,f 

A 

,t  finish  - 

=     0 

Vb 

n 

,f 

,, 

B 

•    A      , 

• 

n 

" 

" 

C 

t          »  t          - 

^300 

n 

FIG.  171.  — Test  of  Magnet  Wire. 

In  curve  0  are  plotted  the  data  of  a  test  on  No.  16 
B.  &  S.  fireproof  wire  which  withstood  the  high  tem- 
perature excellently  except  for  a  slight  discoloration, 
and  was  in  good  shape  at  the  finish.  Its  insulation  re- 
sistance at  start  was  lower  than  any,  but  at  the  finish 
reached  as  high  as  800  megohms. 

After  making  the  tests  it  was  decided  to  use  the  as- 
bestos and  cotton-covered  wire,  and  motor  troubles  were 
practically  ended.  Coils  have  been  opened  up  with  every 


224  SOLENOIDS 

vestige  of  cotton  gone,  yet  the  asbestos  kept  the  insula- 
tion almost  perfect.  The  reason  the  fireproof  wire  was 
not  used  was  on  account  of  its  affinity  for  moisture,  due, 
undoubtedly,  to  the  large  amount  of  silicate  of  soda 
used  in  the  composition  of  its  covering.  In  very  damp 
weather  the  insulation  resistance  would  fall  very  low 
on  this  wire. 

The  wire  in  each  case  was  wound  on  bare  sheet-iron 
spools,  then  joined  in  series,  and  a  current  of  22  amperes 
passed  through  them.  A  thermometer  was  placed  in 
each  coil  and  the  temperature  taken  every  three  minutes. 
The  resistance  was  taken  with  a  Wheatstone  bridge. 
The  thermometers  were  carefully  selected  for  accurate 
reading. 

Another  test,*  described  below,  is  of  interest. 

Investigation  has  shown  that  at  a  temperature  of 
about  147°  C.,  cotton-covered  wire  will  in  time  char  to 
an  extent  that  will  break  down  its  insulation.  It  was 
further  ascertained  that  at  199°  C.  cotton-covered  wire 
will  begin  to  smoke  in  20  seconds.  At  239°  C.  it  was 
distinctly  discolored  in  50  seconds,  and  complete  car- 
bonization had  taken  place  at  245°  C.  in  2  minutes  and 
15  seconds. 

These  temperatures  are,  of  course,  excessive,  yet 
they  go  to  show  how  short  a  space  of  time  is  neces- 
sary to  ruin  the  field  or  armature  windings  on  a 
railway  motor,  subjected  as  they  frequently  are  to 
enormous  overloads.  Deltabeston  wire  tested  under 
identically  the  same  conditions,  in  fact  subjected  to 
identically  the  same  volume  of  current,  is  absolutely 
unaffected. 

An  interesting  comparative  test  of  the  properties  of 
*  D.  &  W.  Fuse  Co. 


INSULATED  WIRES  225 

the  two  wires  is  shown  by  coupling  two  pieces  together 
and  subjecting  them  to  the  same  current,  resulting  in 
the  complete  destruction  of  the  cotton  insulation  while 
not  in  the  least  affecting  the  Deltabeston  wire,  which 
may  be  further  increased  in  temperature  to  a  dull  red 
heat  without  its  insulation  being  destroyed. 

Thus  the  only  limit  to  the  temperature  at  which  this 
wire  may  be  run  is  the  oxidation  of  the  copper  itself, 
which  will  gradually  occur  if  the  coil  is  run  continu- 
ously at  a  copper  temperature  of  250°  C. 

The  fact  that  the  drying  process  of  enameled  wire  is 
carried  out  at  a  temperature  of  more  than  300°  F.  is 
conclusive  proof  that  the  enamel  will  not  be  injured  by 
any  temperature  below  this  value,  and  some  manufac- 
turers claim  their  enameled  wire  will  not  be  impaired 
by  a  temperature  of  500°  F. 

117.  THICKNESS  OF  INSULATION 
The  thickness  of  insulation  on  an  insulated  wire  is 
usually  referred  to  as  the  increase  due  to  insulation. 
As  this  increase  is  commonly  expressed  in  mils  (the 
mil  being  one  thousandth  of  an  inch),  the  increase  is 
usually  referred  to  as  mil-increase. 

For  cotton-covered  *  wires,  the  mil-increase  for  the 
various  sizes  is  usually  as  follows: 

SINGLE-COVERED  DOUBLE-COVERED 

Nos.  0000  to    7     ...     6  mils  12  mils 

8  to  19     ...     5  10 

20  to  36     ...     4  8 

For  silk-covered  *  wires  : 

SINGLE-COVERED  DOUBLE-COVERED 

Nos.  16  to  40    .     .     .     .     2  mils  4  mils 

*  American  Electrical  Works. 


226  SOLENOIDS 


Special  silk  insulation  may  be  obtained  with  1.5  and 
3-mil  insulation,  respectively. 

For  asbestos-covered  wires  (Deltabeston) : 

Nos.    0  to  3 18  mils 

4  to  7 16 

8  to  10 14 

11  to  12 12 

13  to  20 10 

Enameled  wire  *  : 

Nos.  24  to  28  .  .  .  .  0.8  to  1.1  mils 

29  to  33  .  .  .  .  0.7  to  1.0 

34  to  36  .  .  .  .  0.4  to  0.7 

37  to  40  .  .  .  .  0.3  to  0.6 

In  any  event  it  is  well  to  caliper  the  insulated  wire 
with  a  ratchet-stop  micrometer,  to  ascertain  the  in- 
crease in  diameter  due  to  insulation . 

In  the  so-called  bare-wire  winding,  the  least  distance 
between  the  turns  of  wire,  edge  to  edge,  is  3  mils  for 
sizes  from  No.  34  to  No.  40  B.  &  S.  gauge  and  approxi- 
mately one  half  the  diameter  of  the  wire  for  larger 
sizes.  The  paper  commonly  used  for  this  purpose  is 
approximately  1  mil  thick,  and  as  it  is  necessary  to  use 
two  thicknesses  of  paper  between  adjacent  layers,  the 
distance  between  the  layers,  edge  to  edge,  is  2  mils. 

118.    NOTATION  FOR  INSULATED  WIRES 

In  this  book,  the  following  notation  is  used  for  in- 
sulated wires: 

Wf  =  total  weight, 

WL=  weight  per  unit  length, 

*  American  Electric  Fuse  Co. 


INSULATED   WIRES  227 

Wv  =  weight  per  unit  volume, 
lw  =  length  of  wire, 
pL  =  resistance  per  unit  length, 
p{  =  resistance  per  unit  weight, 
pv  =  resistance  per  unit  volume, 
R  ==  total  resistance, 

i  =  increase  in  diameter  due  to  insulation, 
d1  =  diameter  of  insulated  wire,  =  d  +  i,  (201) 

df  =  sectional   area    occupied    by  insulated   wire   and 

interstices  when  coiled  into  a  winding, 
2  =  sectional  area  of  insulation. 

In  practice,  the  value  of  d-f  is  equivalent  to  the 
square  of  the  diameter  of  the  wire  and  insulation  as 
measured  with  a  ratchet-stop  micrometer,  and  the 
charts  on  pp.  314  to  316  are  based  on  this  principle. 

119.    RATIO  OF  CONDUCTOR  TO  INSULATION  IN 
INSULATED  WIRES 

It  is  evident  that 

2  =  0.7854(^2-^2).  (202) 

The  percentage  of  copper  in  an  insulated  wire  will, 
therefore,  be 

percentage  of  copper  =    —  --  —  .  (203) 

For  any  kind  of  round  insulated  conductor  the  per- 
centage of  weight  of  conductor  is 

'         (204) 


wherein      Grs  =  specific  gravity  of  conductor, 
gs  =  specific  gravity  of  insulation. 


228  SOLENOIDS 

The  values  of  gs  are  approximately  as  follows : 
Asbestos  1.6,  cotton  1.4,  silk  1.0.  Owing  to  their 
hygroscopic  properties  the  data  obtained  from  the 
above  materials,  when  thoroughly  dry,  are  liable  to 
appear  rather  low. 

The  weight  per  unit  volume,  Wv,  for  insulated  wires 
may  be  readily  determined  by  the  equation 

Wv  =  &,  (205) 

Pi 

wherein        pv  =  resistance  per  unit  volume, 
and  pi  =  resistance  per  unit  weight. 

Wv  may  be  considered  as  the  combined  weight  and 
space  factor.  (See  Fig.  215,  p.  309.) 

120.    INSULATION  THICKNESS 

When  the  size  of  wire  and  resistance  per  unit  volume 
are  fixed,  the  required  thickness  of  insulation  may  be 
found  by  the  equation 

<->g-*  (206) 

wherein  c  =  2192  x  10~8  in  metric  units,  and  86,284  x 
10~n  in  English  units. 


CHAPTER   XVIII 

ELECTROMAGNETIC   WINDINGS 

121.    MOST  EFFICIENT  WINDING 

AN  electromagnetic  winding  consists  of  an  assem- 
blage of  helices  of  insulated  wire,  in  a  definitely  pre- 
pared space  surrounding  the  core,  the  direction  of  the 
turns  being  alternately  right  and  left ;  that  is,  the  turns 
do  not  lie  exactly  at  right  angles  with  the  core  as  they 
should  theoretically. 

The  most  efficient  winding  is  that  which  has  the 
maximum  number  of  turns  of  wire  for  the  minimum  re- 
sistance ;  consequently  that  which  has  the  maximum 
ampere-turns  for  a  minimum  voltage. 

In  an  ideal  winding,  the  mass  of  conducting  material 
would  exactly  equal  the  winding  space.  There  would 
be  no  space  lost  due  to  insulation,  which  would  be  in- 
finitesimal, and  there  would  be  no  interstices  between 
adjacent  turns  or  between  adjacent  layers. 

Even  with  ideal  conditions,  however,  there  could  be 
but  two  cases  where  no  space  would  be  lost  due  to  the 
turning  back  of  one  layer  upon  another.  In  the  first 
case,  the  winding  would  consist  of  but  one  turn  of 
square  or  rectangular  wire,  forming  a  hollow  cylinder, 
while,  in  the  second  case,  the  winding  might  consist  of 
an  infinite  number  of  turns  of  square  wire  whose  cross- 
section  should  be  vanish ingly  small. 

Before  departing  from  the  discussion  of  ideal  condi- 
tions, which  is  given  to  show  what  a  thoroughly  prac- 

229 


230 


SOLENOIDS 


tical  proposition  an  electromagnetic  winding  really  is,  a 
comparison  of  the  cross-sections  of  windings  of  round 
and  square  wires  may  be  appreciated  by  referring  to 


<—  a—  > 

FIG.  173. 
Space  Utilization  of 
Square  Wire. 

FIG.  172. 

Space  Utilization  of 
Round  Wire. 

Figs.  172  and  173,  in  which  the  winding  volumes  are 
the  same  in  both  cases.  For  the  same  number  of  turns, 
then,  the  amount  of  copper  in  the  winding  in  Fig.  172 
will  only  contain 

^  =  0.7854 

of  that  in  Fig  173,  the  dimension  a  being  the  same  in 
both  cases. 

In  practice,  there  is  no  such  thing  as  infinitesimal 
insulation  ;  hence,  there  are  interstices  between  adja- 
cent turns  and  between  adjacent  layers. 

While  wires  of  square  cross-section  are  sometimes 
used,  in  the  larger  sizes,  on  the  field  magnets  of  motors, 
etc.,  and  wires  or  ribbons  of  rectangular  cross-section 
are  also  used  in  certain  cases,  which  will  be  discussed 
further  on,  the  magnet  wires  commonly  used  are  cir- 
cular in  cross-section,  and,  in  this  book,  the  latter  form 
of  wire  will  be  assumed  unless  otherwise  stated. 

The  reason  for  using  a  round  wire  is  on  account  of 
the  tendency  of  the  square  wires  to  lie  upon  their  cor- 


ELECTROMAGNETIC   WINDINGS  231 

ners,  as  well  as  upon  their  flat  faces,  and  for  the  further 
reason  that,  as  the  periphery  of  a  square  or  rectangle  is 
greater  than  that  of  a  circle,  for  equal  areas,  the  extra 
amount  of  insulation  necessary  to  cover  the  wire  takes 
up  more  of  the  winding  volume  for  the  square  or  rec- 
tangular conductors  than  for  the  round  wire. 

No  matter  what  the  form  of  a  winding  space  may  be, 
there  are  three  dimensions  which  must  always  be  con- 
sidered ;  viz.  the  average  length  of  all  the  turns  (j?a), 
the  interflange  length  (Z),  or  the  length  of  the  wind- 
ing, and  the  depth  or  thickness  (3T)  of  the  winding. 
The  volume  or  cubical  contents  of  any  form  of  winding 
space  may  then  be  expressed 

V=PaLT.  (207) 

It  may  be  well  to  state  here  that  the  number  of  turns 
in  an  ideal  case  are  proportional  to  one  half  the  longi- 
tudinal cross-section  of  the  winding,  divided  by  the 
sectional  area  occupied  by  the  insulated  wire,  or 

N=.  (208) 


The  turns  per  unit  longitudinal  cross-sectional  area 
of  winding  are 


l 
Hence,  N=  TLNa,  (210) 

The  resistance  may  be  expressed, 

R  =  Pap,N,  (211) 

wherein  pa  is  the  average  length  of  all  the  turns,  and 
p,  is  the  resistance  per  unit  length  of  wire. 


232  SOLENOIDS 

122.   IMBEDDING  OF  LAYERS 

In  the  round-wire  winding,  the  layers  have  a  tend- 
ency to  imbed.  At  the  point  where  the  turns  of  ad- 
jacent layers  cross  one  another  they  appear  as  in  Fig. 
172.  Diametrically  opposite  this  point  there  is  another 


FIG.  174.  FIG.  175. 

Space  Utilization  of  Imbedded  Relations  of  Imbedded 

Wires.  Wires. 

crossing  point,  but  at  the  ends  of  a  diameter  at  right 
angles  with  this  one,  the  turns  of  the  upper  layers 
occupy  the  space  between  the  layers  beneath,  as  in 
Figs.  174  and  175. 

Theory  indicates  that  there  should  be  a  gain  of  7.2 
per  cent  in  turns  on  account  of  this  imbedding.  How- 
ever, the  insulation  is  compressed,  owing  to  the  verti- 
cal tension,  which  fact  causes  it  to  occupy  more  space 
latterly  than  calculated. 

As  a  test  *  of  the  imbedding  theory,  the  author  had 
constructed  a  solid  bobbin  of  steel  exactly  2.54  cm. 
between  the  faces  of  the  heads,  and  with  a  core  1.27  cm. 
in  diameter.  This  was  wound  by  hand,  by  an  expe- 
rienced operator,  with  various  sizes  of  single-silk-cov- 
ered magnet  wire  ranging  from  Nos.  21  to  34  B.  &  S. 
gauge.  The  values  for  dl  in  Fig.  176  were  taken  with 
a  ratchet-stop  micrometer.  This  shows  the  relation  (for 
*  Electrical  World,  Vol.  53,  No.  3,  1909,  pp  155-157. 


ELECTROMAGNETIC    WINDINGS 


233 


eight  layers)  between  thickness  of  winding  2*  and  cali- 
pered  diameter  of  insulated  wire.  Ev,en  with  7.2  per 
cent  allowed  for  im- 
bedding, there  was 
found  to  be  an  ad- 
ditional "flattening 
out  "of  the  insulation,  j 

vertical    ^ 

of     the 

to    the 


due  to  the 
compression 
wire,  owing 
tension.  This  aver- 
aged approximately 
6  per  cent. 

For     a     constant 
thickness    of    insula- 


.02 


.04 


.06 
(cms.) 


.08 


.10 


FIG.  176. — Test  of  an  8-layer  Magnet 
Winding. 


tion,  it  would  appear  that  this  effect  would  vary  with 
different  sizes  of  wire;  but  since  the  tension  on  the 
wire  during  the  winding  process  decreases  as  the  diam- 
eter of  the  wire  decreases,  it  remains  practically  constant 
for  the  sizes  of  wire  mentioned  above.  Examination  of 
the  wire  when  removed  from  the  experimental  winding 
showed  that  the  wire  had  not  been  appreciably  stretched 
in  winding.  This  apparent  gain  of  approximately  6  per 
cent  was  found  to  be  compensated  by  a  loss  of  approxi- 
mately 6  per  cent  in  the  turns  per  unit  length. 

The  formula  used  for  calculating  the  actual  average 
thickness  of  the  winding  per  layer  is 


_  _ 
0.933O  -!)  +  !' 

wherein  n  =  the  number  of  layers,  and  T  the  thickness 
or  depth  of  winding. 

It  will  be  observed  that  in  this  formula  an  allowance 
of  7.2  per  cent  has  been  made  for  imbedding. 


234  SOLENOIDS 

By  transposition, 

/T7         \ 

»  =  1.072^  -lj+1, 

and  ^=£[0.933  (w-l)  +  1]. 


(213) 
(214) 


123.    Loss  AT  FACES  OF  WINDING 


The  loss  at  the  faces  or  ends  of  the  winding,  due  to 
the  turning  back  of  one  layer  upon  another,  is  propor- 
tional to  the  turns  per 
layer.     There  is  a  loss 


100 


80 


20 


of 


0  +  1 


or  one  half 


'20  .40  60  .60          100 

mL 
FIG.  177.  — Loss  of  Space  by  Change  of 

Plane  of  Winding.  loss  = 


turn  at  each  end,  or 
one  turn  per  layer. 

The  percentage  of 
loss,  due  to  this  effect, 
is  equal  to  the  loss  in 
turns  per  layer  divided 
by  the  turns  per  layer, 
or 
per  cent 


mL' 


(215) 


wherein  m  represents  the  turns  per  unit  length,  and 
L  is  the  length  of  the  winding.  Figure  177  shows  that 
while  this  loss  is  not  great  for  small  wires,  it  may  be 
considerable  for  large  wires  where  L  has  a  small  value. 

124.   Loss  DUE  TO  PITCH  OF  TURNS 

Another  effect  which  is  very  important,  and  which 
explains  why  the  insulated  wire  should  be  wound 
evenly  in  layers,  is  the  loss  in  magnetizing  force,  for  a 


ELECTROMAGNETIC   WINDINGS  235 

given  length  of   wire,  when  the  wire  is  not  at   right 
angles  with  the  core. 

All  other  things  being  constant,  the  winding  having 
the  highest  efficiency  will  contain  the  greater  number 
of  turns  for  a  given  resistance  ;  but  a  piece  of  wire 
having  a  given  resistance  may  be  so  arranged  in  a 
corresponding  winding  space  that  there  will  not  be  one 
effective  turn. 

As  an  extreme  case,  consider  a  core  wound  longitu- 
dinally and  uniformly  with  insulated  wire.  It  is  ap- 
parent that  the  turns  in  this  case  are  not  effective  for 
magnetizing  the  core  longitudinally,  in  the  ordinary 
sense. 

In  an  ideal  case  the  conductor  would  be  at  right  angles 
to  the  longitudinal  center  of  the  winding,  as  in  Fig.  178, 
but  in  all  practical  windings  there  is  a  tend- 
ency of  the  conductors  to  incline   toward 
the   longitudinal    center   of    the    winding. 
This  inclination  depends  upon  the  diameter  ' 
of  the  turn  and  the  diameter  of  the  insulated 
wire,  for  layer  windings.     It  is  important 
to  always  consider  the   inclination  of  the     FlG  178  _ 
average  turn,  as  the  inclination  is  greater     ideal  Turn, 
for  the  inner  turns,  and  less  for  the   outer  turns,  as 
compared  with  the  diameter  of  the  average  turn. 

In  an  ideal  case  the  number  of  turns  would  be  deter- 
mined by 

or     N=  TLNa ;         (210) 


but,  while  (208)  may  hold  near  enough  for  many  cases 
in  practice,  it  is  important  to  consider  the  inclination 
of  the  turns,  referred  to  above,  when  dealing  with  certain 
cases. 


236  SOLENOIDS 

When  the  inclination  is  considered,  the  number  of 
turns  cannot  be  calculated  directly  by  (208),  but  the 
ratio  r  may  be  determined  by 

r=-  -2-  -,  (216) 


wherein  Mis  the  average  diameter  of  all  the  turns  in 
a  round  winding,  and  represents  the  average  perimeter 
divided  by  TT  for  any  other  form  of  winding  space. 

Hence,         M=&     (217)     =QMSpa.  (218) 

7T 

In  "haphazard"  or  similar  windings,  the  pitch  or 
inclination  may  be  so  great"  that  the  distance  between 
adjacent  turns,  which  we  may  designate  by  d^  may  even 
exceed  M.  In  this  case 

(216) 


The  number  of  turns  in  any  winding  and  with  any 
pitch  is 


(219) 
d1 
Substituting  the  value  of  r  from  (216)  in  (219), 

(220) 


When  dl  =  M,  the  pitch  would  appear  as  in  Fig.  179. 
When  M  is  great  as  compared 
with  dt,  the  ratio  r  will  be  near 
--  unity,  but  when  dl  is  greater  than 

,,-  \  i  \  i  M,  r  has  a  low  value.  In  Fig. 

180  is  shown  the  percentage  of 

FIG.  179.  —  Pitch  when  dt=M.  & 

turns  for  various  ratios  or  dt  to 

M,  the  size  of  insulated  wire  and  resistance  remaining 
constant. 


ELECTROMAGNETIC   WINDINGS 


237 


Figure  180  shows  very  clearly  that  an  electromagnetic 
winding  should  be  wound  with  the  turns  as  close  to- 


1  

•  —  •-. 

•  

—  —  „ 

~^- 

^ 

"^ 

^_ 

^^^- 

^-~. 

^^^ 

"^~ 

-  — 

-== 

"-^^. 

-^^: 

•—  — 

— 

)      .1      .2     .3     A     .5       6      .7     A     .9      1     1.1    1.2   1.3   1.4    1.5    1.6   1.7    1.8  1.9    2 

Values  of  ^r 
iVl 

FIG.  180.  — Effects  Due  to  Pitch  of  Winding. 

gether,  and  as  near  at  right  angles  with  the  core,  as 
possible. 

125.    ACTIVITY 

It  is  seen,  then,  that  there  are  several  factors  which 
prevent  the  mass  of  conducting  material  from  equaling 
the  entire  available  winding  space.  Since  a  round  wire 
is  used  in  practice,  only  about  75  per  cent  of  the  wind- 
ing space  may  be  utilized,  even  with  the  larger  sizes  of 
wire,  which  represents  a  loss  of  approximately  25  per 
cent.  While  there  is,  theoretically,  a  gain  of  7.2  per 
cent,  due  to  imbedding,  this  is  usually  neutralized  by 
deformities  in  practical  windings.  Then  there  is  the 
loss  at  the  ends,  due  to  turning  back.  This  loss  may 
be  ignored  in  fine-wire  layer  windings,  and  generally, 
in  windings  of  considerable  length.  The  inclination 
of  the  turns  may  not  be  considered  in  practice,  where 
a  uniform,  fine-wire  layer  winding  is  employed,  but 
this  is  extremely  important  in  "haphazard"  windings. 


238 


SOLENOIDS 


It  is  apparent,  then,  that  the  thickness  of  the  insu- 
lation on  the  wire  is  the  principal  point  to  be  considered 
in  connection  with  practical  round-wire  windings,  so 
far  as  space  utilization  is  concerned. 

The  coefficient  of  space  utilization  or  Activity  is  the 
ratio  between  total  cross-section  of  copper  and  the 
total  cross-section  of  winding  space.  In  this  it  is  as- 
sumed that  the  turns  are  at  right  angles  to  the  core. 
Therefore,  the  practical  rule  is  better  expressed  as 
follows  : 

^0.7864^  (221) 

wherein  ty  is  the  activity. 

In  this  the  total  turns  are  multiplied  by  the  sectional 
area  of  the  wire,  to  give  the  total  sectional  area  of  the 
copper  in  the  winding. 

For  the  ideal   winding  i/r=l  or  100  per   cent.     In 


Size  of  Wire.  B  &  S.  Gauge 

FIG.  181.  —  Weight  of  Copper  in  Insulated  Wires. 

practice,  -fy  may  be  as  high  as  0.75  with  very  coarse 
round-wire   field-magnet   windings,  while  in  fine-wire 


ELECTROMAGNETIC   WINDINGS  239 

coils  it  may  be  as  low  as  0.2,  depending  upon  the  thick- 
ness of  insulation  and  the  regularity  of  winding. 

The  space  occupied  by  the  insulation  on  the  wires, 
as  well  as  other  interstices,  may  be  appreciated  by  con- 
sulting Fig.  181.  It  may  be  noted  that  a  No.  37  B.  &  S. 
wire,  insulated  with  silk  to  a  1.5-mil  increase,  has  twice 
as  much  copper  per  unit  winding  volume  as  the  same 
wire  insulated  with  cotton  or  silk,  to  a  4-mil  increase. 

126.   AMPERE-TUKNS  AND  ACTIVITY 

The  ampere-turns  in  a  winding  are  constant  when 
the  size  of  the  wire,  length  of  the  average  turn  (j?a), 
and  voltage  across  the  terminals  of  the  winding  are 
constant,  and  regardless  of  the  number  of  turns  and, 
consequently,  the  activity. 

127.   WATTS  AND  ACTIVITY 

However,  the  insulation  should  be  kept  as  thin  as 
permissible,  so  as  to  have  as  much  copper  in  the  wind- 
ing as  possible,  as  the  cost  of  operating  and  heating  will 
vary  with  the  actual  resistance  in  the  winding,  or  in 
any  specific  case,  with  the  actual  weight  of  copper. 
Therefore  the  thinner  the  insulating  material,  the  less 
will  be  the  heating,  and,  consequently,  the  cost  of  oper- 
ating, as  heat  in  a  winding  is  lost  energy,  and  expensive 
at  that. 

For  this  reason,  the  custom  of  removing  wire  from 
the  outside  of  a  winding  to  reduce  the  average  perime- 
ter, and  thus  increase  the  ampere-turns,  is  poor  practice 
and  very  inefficient,  as  the  heating  is  increased  many 
times  for  only  a  slight  gain  in  ampere-turns,  and  the 
cost  of  operating  increases  in  exactly  the  same  ratio  as 
the  amount  of  wire  in  the  winding  decreases,  since 


240  SOLENOIDS 

watts  vary  inversely  as  the  resistance,  for  constant 
voltage.  With  constant  current,  the  cost  of  operating 
varies  directly  with  the  resistance  of  the  winding,  but 
taking  off  any  of  the  turns  would  reduce  the  ampere- 
turns  proportionately. 

In  a  specific  case,  if  100  volts  be  applied  to  a  wind- 
ing consisting  of  7620  turns  of  No.  30  single-cotton- 
covered  wire,  with  a  resistance  of  205  ohms,  3T10 
ampere-turns  will  be  produced  at  an  energy  expenditure 
of  48.7  watts.  If  now,  one  half  of  the  turns  be  removed, 
leaving  3810  turns,  and  a  resistance  of  77  ohms,  4950 
ampere-turns  will  be  produced,  at  an  expenditure  of  130 
watts. 

Therefore,  to  increase  the  ampere-turns  33  per  cent, 
the  cost  of  operating  has  been  increased  2.67  times; 
although  the  cost  of  the  wire  has  been  reduced  in  the 
same  proportion.  Hence,  if,  say,  20  per  cent  is  saved  in 
the  cost  of  the  wire,  it  will  cost  20  per  cent  more  to 
operate  the  electromagnet. 

128.   VOLTS  PER  TURN 

A  winding,  with  internal  and  external  dimensions 
constant,  may  be  wound  with  any  size  of  insulated  wire, 
and  by  varying  the  voltage  across  the  terminals  of  the 
winding,  the  ampere-turns  may  be  kept  constant  also. 

If  bare  wire  were  used,  as  in  the  ideal  case,  or  if  the 
ratio  of  copper  to  insulation  was  constant,  the  volts  per 
turn  would  also  be  constant.  This  may  be  readily 
understood  when  it  is  remembered  that  the  resistance 
of  the  conductor  varies  inversely  as  its  cross-section, 
and  that  the  number  of  turns  vary  inversely  as  the 
cross-section,  also.  Hence,  if  a  winding  contained  but 
one  turn  of  wire,  with  a  resistance  of  one  ohm,  and  an 


ELECTROMAGNETIC   WINDINGS  241 

e.  m.  f.  of  one  volt  was  applied  to  it,  there  would  result 
one  ampere-turn.  Now  if  the  same  space  were  occupied 
by  two  turns,  the  resistance  per  turn  would  be  doubled  ; 
i.e.  the  total  resistance  would  be  four  ohms.  With 
one  volt  per  turn,  the  e.  m.  f.  would  be  two  volts  ;  hence, 
the  current  would  be  one  half  ampere,  and  there  would 
be  but  one  ampere-turn,  as  before.  In  practice,  the 
volts  per  turn  vary  inversely  with  i/r. 

129.    VOLTS  PER  LAYER 

What  really  determines  the  necessary  dielectric 
strength  of  the  insulation  on  a  wire  are  the  volts  per 
layer,  or,  to  be  exact,  the  e.  m.  f. 
between  ends  of  two  adjacent 
layers,  as  between  the  points  OOOOOOOOOOO 

#-6,  Fig.  182.  FIG.  182.  — Showing  where  the 

Since   there   are   more   turns       Greatest  Difference  of  Poten- 

,  •  n  •  -1         tial  Occurs, 

per  layer  in  a  fine-wire  wind- 
ing than  in  a  coarse-wire  winding,  the  e.  m.  f.  be- 
tween adjacent  layers  will  be  much  greater  for  the 
former  than  for  the  latter  for  the  same  number  of  turns 
and  volts.  Hence,  it  is  obvious  that  where  fine  wires 
are  used,  the  activity  is  necessarily  less  than  for  coarser 
wires,  although  the  mechanical  properties  of  the  insu- 
lation must  not  be  neglected. 

The  e.  m.  f .  per  layer  is  found  by  dividing  the  voltage 
across  the  terminals  of  the  winding  by  the  number  of 
layers.  This,  however,  only  gives  the  average  e.  m.  f. 
per  layer.  What  is  more  important  is  to  find  the 
maximum  voltage  between  any  two  layers.  This  will 
naturally  be  at  the  outer  layers.  Hence,  to  find  the 
maximum  e.  m.  f.  between  the  two  outer  layers,  multi- 


242 


SOLENOIDS 


ply  the  e.  m.  f .  between  two  average  layers  by  the  ratio 
between  the  outer  and  average  perimeters,  thus, 

em  =  ^  (222) 

wherein  em  is  the  maximum  e.  m.  f .  between  the  two 
outer  layers,  pm  the  mean  perimeter  of  the  two  outer 
layers,  n  the  number  of  layers,  and  pa  the  average 
perimeter  of  all  the  layers. 

When  a  winding  is  to  be  designed  to  fill  a  long  wind- 
ing space,  it  should  be  divided  into  sections  so  as  to 
keep  the  maximum  e.  m.  f .  between  any  two  layers  as 
low  as  possible.  This  will  be  discussed  further,  in  the 
proper  place. 

130.   ACTIVITY  EQUIVALENT  TO  CONDUCTIVITY 

Thus  far  the  relation  of  space  occupied  by  the  con- 
ductor and  the  insulation  covering  it  have   not  been 
i.o 


0.1 


"10      12     14      16 


18   20   22   24  26   28   30  32   34  36   38  40 

Size  of  Wire,  B  &  S  Gauge 
FIG.  183.  —  Loss  of  Space  by  Insulation  on  Wires. 

considered.     The  activity  ratio  or  practical  activity  for 


ELECTROMAGNETIC   WINDINGS 


243 


round  wires  is  — -•     Figure  183  shows  the  activity  and 

6ti 

the  activity  ratios  for 
insulated  round  wires. 
In  this,  the  other  fac- 
tors, such  as  imbed- 
ding, etc.,  are  not 
considered. 

The  activity  of  an 
electromagnetic  wind- 
ing is  equivalent  to 
the  conductivity  of 
the  conductor  itself, 
where  the  dimensions 
of  the  winding  space 
are  limited.  This  may 
be  appreciated  by  reference  to  Figs.  184  and  185.  In 
Fig.  184  the  turns  and  length  of  wire  are  constant,  and 
100 1 1 1 , ^,  the  resistance  and  size 

of  wire  are   variable. 

In  this  case,  if  a  given 
•^x^  /  winding  space  be  oc- 

6o  I |_^o*4__        — _/(_  cupied  by,  say,  5000 

turns,    with    a   coeffi- 


FIG.  184. — Characteristics  of  Winding  of 
Constant  Turns  and  Length  of  Wire. 


20 


~~C 
& 


& 


fH 


1.0 


FIG.  185.  —  Characteristics  of  Winding  of 
Constant  Resistance. 


cient    of     -—  =  0.25, 

di 
and  an  exactly  similar 

winding  space  con- 
tains 5000  turns,  but 
with  the  coefficient  of 

— -=0.5,    the    latter 


winding  will  contain  the  same  number  of  turns  and  length 


244 


SOLENOIDS 


of  wire  as  the  former,  but  will  have  only  one  half  the  re- 
sistance, with  the  cross-section  of  the  wire  doubled.  Here 
the  size  of  wire  varies  directly,  and,  consequently,  the 

resistance  varies  inversely  as  —  •    Hence,  with  constant 

e.  m.  f.,  the  m.  m.  f.  and  watts  will  vary  directly  as  —  • 

In  Fig.  185  the  resistance  is  constant,  and  the  turns,  . 
cross-section,  and  length  of  wire  are  variable.     In  this 
case   the    number  of   turns   and   length   of  wire  vary 

directly  as  A/ — •>    and   the    cross-section    of    the   wire 
^i 

varies   directly  as  (  — -  ]  •     With    constant  e.  m.  f.  the 
\»i  / 

m.   m.   f.     will     vary 

ra 

directly  as  -y — ^  anc^ 
d1 

the  watts  will  remain 
constant. 

In  Fig.  186  the 
cross-section  of  wire 
is  constant,  and  the 
resistance,  turns,  and 
length  of  wire  are  vari- 
able. It  is,  of  course, 
LO  obvious  that  the 
three  variables  vary 

FIG.  186.  —  Characteristics  of  Winding  of 

Constant  Cross-section  of  Wire.  directlv  as  '    With 

d-? 
constant  e.  m.  f.,  the  m.  m.  f.  will  be  constant,  and  the 

watts  will  vary  inversely  as  — -• 

dl 


ELECTROMAGNETIC   WINDINGS 


245 


131.    RELATIONS   BETWEEN   INNER  AND   OUTER  DI- 
MENSIONS   OP    WINDING,    AND    TURNS,    AMPERE- 
TURNS,  ETC. 
The  effect  of  an  increased  activity  is  more  marked  in 

100 

90 


FIG.  187. — Effect  upon  Characteristics  of  Windings  of 
Varying  the  Perimeters. 

a  winding  of  small  than  of  large  diameter,  and  varies 
directly  with  the  length,  L,  of  the  winding.  Figure 
187  shows  the  various  relations,  ^>min  and  jomax  being  the 
minimum  and  maximum  perimeters  respectively  ;  pa 
the  average  perimeter,  and  T  the  thickness  or  depth 
of  the  winding. 

132.    IMPORTANCE  OF  HIGH  VALUE  FOR  ACTIVITY 

In  order  to  make  the  operation  of  an  electromagnetic 
winding  economical,  it  is  readily  seen  that  ty  should 
have  as  high  a  value  as  possible,  since  increasing  the 
turns,  for  a  given  size  of  wire,  will  not  change  the 


246  SOLENOIDS 

ampere-turns,  but  will  increase  the  resistance  ;  thus 
reducing  the  current  and,  consequently,  the  cost  of 
operating. 

In  any  case,  when  designing  coils  which  are  to  be  in 
use  continuously,  only  the  thinnest  and  best  insulation 
should  be  used,  for  the  cost  of  operating  will  vary  in 
direct  proportion  to  the  amount  of  copper  saved  by 
using  coarse  insulation  ;  therefore,  it  pays  to  use  more 
copper  and  less  current.  Moreover,  the  heating  effect 
decreases  as  the  amount  of  copper  is  increased,  for  the 
same  number  of  ampere-turns. 

When  the  current  is  to  be  on  the  winding  but  for  a 
brief  period,  and  when  the  time  between  operations  is 
long,  the  saving  in  copper  is  not  so  important,  as  the  in- 
creased cost  of  the  current  may  not  be  worth  considering. 

133.  APPROXIMATE  RULE  FOR  RESISTANCE 

The  resistance  of  the  same  kind  of  insulated  wire 
which  will  occupy  a  given  winding  space  varies  ap- 
proximately 50  per  cent  for  consecutive  sizes  of  wire 
and  approximately  100  per  cent  for  every  two  sizes. 
This  is  often  convenient  for  mentally  estimating  the 
size  of  wire  to  use  when  the  resistance  of  a  similar 
winding,  but  with  a  different  size  of  wire,  is  known. 

134.  PRACTICAL  METHOD  OF  CALCULATING 

AMPERE-TURNS 

The  following  method  is  convenient  for  calculating 
ampere-turns.  In  this  method,  use  is  made  of  the 
factor  M,  which  is  really  the  average  diameter  of  a 
circular  winding.  In  any  form  of  winding,  however, 

M=£*.  (223) 

7T 


ELECTROMAGNETIC   WINDINGS 


247 


In  the  American  wire  gauge  (B.  &  S.)  the  cross-sec- 
tional area  of  the  wires  varies  nearly  in  the  ratio  of  10 
for  every  ten  sizes,  the  real  ratio  being  10.164  :  1.  On 
this  basis  Fig.  188  has  been  plotted,  the  values  for  wires 
from  No.  20  to  No.  30  being  correct  ;  but  for  wires 
from  No.  10  Co  No.  20  and  between  No.  30  and  No.  40 


FIG.  188.  —  Ampere-turn  Chart. 

the  values  are  correct  within  1.64  per  cent,  which  is 
near  enough  in  practice,  owing  to  the  gaps  between 
consecutive  sizes  of  wires. 

The  ampere-turns  may  be  quickly  found  by  this 
method  in  the  following  manner :  First  find  the  ratio 
Kf  by  dividing  the  voltage  across  the  winding  by  M,  or 


Then  by  comparing  the  value  of 

K-V- 
fM 


(224) 


(225) 


248  SOLENOIDS 

with  the  desired  ampere-turns,  the  proper  size  of  wire 
(B.  &  S.)  will  be  found  under  the  value  of/,  which 
value  will  be  either  10,  102,  or  103  for  the  sizes  indi- 
cated in  Fig.  188.  It  is  well  to  note  here  that  when 
/  =  10,  the  values  are  for  wires  from  No.  10  to  No.  20, 
and  when/  =  102,  the  values  are  for  wires  from  No.  20 
to  No.  30,  etc.  When  the  value  of 

K-V- 

fM 

exceeds  the  values  of  the  points  of  intersection  on  the 
chart,  divide  this  value  by  10,  and  multiply  the  corre- 
sponding value  of  ampere-turns  by  10,  or  multiply  the 
value  of  /  by  10,  according  to  whether  the  size  of  wire 
or  ampere-turns  is  fixed. 

The  above  is  deduced  from  the  equation 

IN=  —  .  (226) 

PlPa 

135.    AMPERE-TURNS  PER  VOLT 

It  is  often  convenient,  when  designing  windings  for 
different  voltages,  but  for  the  same  type  of  electromag- 
net, to  estimate  the  ampere-turns  per  volt.  The  total 
ampere-turns  may  then  be  easily  calculated  from  the 
total  voltage.  The  chart,  Fig.  188,  will  materially  aid 
in  this  operation. 

136.    RELATION  BETWEEN  WATTS  AND  AMPERE- 
TURNS 

It  can  be  shown  that  the  ratio  of  watts  to  ampere- 
turns  is  simply  the  ratio  of  voltage  to  turns. 

Since  P=  .#7(227),     /=  ?  (228) 


ELECTROMAGNETIC   WINDINGS  249 

Multiplying  both  sides  of  the  equation  in  (228)  by  N, 

(229) 


PN 


FIG.  189.  —Chart  showing  Ratio  between  Watts  and  Ampere-turns. 

and  since 


whence 


;    (231) 
.  (234) 


Therefore,  the  watts  may  be  calculated  from  the 
ampere-turns  when  the  other  constants  are  known,  and 
vice  versa. 


250  SOLENOIDS 

Hence,  to  calculate  watts    from  ampere-turns,  mul- 

rr 

tiply  ampere-turns  by   —  ;  and   to    calculate   ampere- 
turns  from  watts,  multiply  watts  by  —  • 

Figure  205  shows  this  relation  very  nicely.  The 
upper  curve  represents  the  theoretical  ratio,  for  a 
specific  case,  between  watts  and  ampere-turns  for  all 
sizes  of  wire,  no  allowance  being  made  for  imbedding, 
etc.,  and  assuming  that  d^  =  d2  ;  i.e.  i/r  =  0.7854.  It 
will  be  noticed  that  all  the  other  wires  shown  in  curves 
have  4-mil  insulation.  Thus  to  produce  9000  ampere- 
turns  would  require  an  expenditure  of  approximately 
87  watts  for  any  size  of  round  bare  wire  ;  165  watts 
for  a  No.  25  wire  insulated  to  a  4-mil  increase,  and  465 
watts  for  a  No.  40  wire  insulated  to  a  4-mil  increase. 

137.    CONSTANT   RATIO  BETWEEN  WATTS   AND  AM- 
PERE-TURNS, VOLTAGE  VARIABLE 

When  it  is  desired  to  change  the  winding  of  a  coil 
which  will  produce  a  required  number  of  ampere-turns 
at  an  expenditure  of  a  certain  number  of  watts,  with  a 
given  voltage,  so  that  it  shall  produce  the  same  ampere- 
turns  with  the  same  watts  on  any  other  voltage,  it  is 
necessary,  besides  using  a  different  size  of  wire,  to 
change  either  the  average  perimeter,  the  length  of  the 
winding,  or  the  thickness  of  the  insulation  on  the  wire, 
since  the  ratio  of  copper  to  insulation  varies  with  the 
size  of  the  wire. 

The  practical  method  is  to  change  the  length,  L,  of 
the  winding,  which  will  vary  inversely  with  the  activ- 
ity of  the  winding.  Consequently,  for  fixed  average 

perimeter  and  voltage,  L  is  proportional  to  ^ . 


u rai  v  c. n 0 1  i   » 

OF 
LUFOBB^ 

ELECTROMAGNETIC   WINDINGS  251 

138.    LENGTH  OF  WIRE 
The  length  of  wire  in  a  winding  is 
Y 

wherein  V—  volume  of  winding  space, 
and        c?j2  =  cross-sectional  constant, 

Na  =  turns  per  unit  longitudinal  cross-sectional 
area  of  winding. 

If  the  length  of  the  wire  and  the  volume  of  the 
winding  space  are  known,  then  the  cross-sectional  con- 
stant may  be  found  by  transposition. 

d*  =  ~  (237),     whence  Na  =  ^ .          (238) 

139.   RESISTANCE  CALCULATED  FROM  LENGTH  OF 
WIRE 

As  the  resistance  of  an  electrical  conductor  of  con- 
stant cross-section  varies  directly  with  its  length,  it  is 
evident  that  the  resistance  of  any  wire  which  may  be 
contained  in  a  bobbin  or  winding  volume  may  be  readily 
calculated  by  multiplying  the  length  of  the  wire  by  the 
resistance  per  unit  length,  pt. 

Thus,  E  =  lwPl.  (239) 

Values  for  pt  for  the  various  sizes  of  wires  are  given 
in  the  tables  in  Chap.  XXI. 

When  using  metric  units,  the  ohms  per  meter  may,  of 
course,  easily  be  changed  to  ohms  per  centimeter  by 
simply  dividing  the  former  by  10.  As  the  American 
wire  table,  in  English  units,  on  p.  305  expresses  the  re- 


252  SOLENOIDS 

sistance  per  unit  length  as  ohms  per  foot,  this  will  have 
to  be  divided  by  12  to  reduce  it  to  ohms  per  inch. 

Likewise,  the  kilograms  per  meter  and  pounds  per  foot 
must  be  reduced  to  the  same  units  as  used  in  calculating 
the  dimensions  of  the  winding  space. 

140.    RESISTANCE  CALCULATED  FROM  VOLUME 

77- 

Since    the  length   of   the  wire  =  lw  =  —    (235),    or 

*i 

lw=VNa  (236),    (239)   becomes   ^=          (240),    or 


When    F=  1,  R  =  -^-\  hence,  it  is  evident  that  A 
d*  d? 

represents  the  resistance  per  unit  volume  to  which  pv  is 
assigned. 

Therefore,  Pv  =  -jfr  (242),  or  Pv  =  PlNa.  (243) 

It  is  then  a  simple  matter  to  calculate  the  resistance, 
when  the  other  constants  are  known,  by  multiplying 
the  volume  of  the  winding  by  the  resistance  per  unit 
volume  : 

Thus,  R  =  pvV.  (244) 

For  values  of  pv  see  charts,  pp.  314-316. 

The  proper  value  for  pv,  to  produce  the  required  re- 

sistance in  a  given  winding  volume,  may  be  determined 

-p 
by  rearranging  (244),  whence  pv=  —  .  (245) 

The  charts,  pp.  314-316,  show  the  ohms  per  cubic  inch 
for  various  diameters  of  copper  wire,  irrespective  of  the 
gauge  number,  with  various  increases  in  diameter  due 
to  insulation.  For  convenience,  the  different  sizes  of 
wire  of  B.  &  S.  gauge  are  shown  in  dotted  lines,  in 
positions  corresponding  to  their  diameters. 


ELECTROMAGNETIC   WINDINGS  253 

As  an  example  of  the  use  of  these  charts,  refer  to 
Fig.  218,  and  assume  that  an  insulated  copper  wire  is  de- 
sired which  shall  have  a  resistance  of  4  ohms  per  cubic 
inch  when  wound  on  a  bobbin. 

Tracing  vertically  upward  from  4,  it  will  be  found 
that  this  result  is  obtained  with  a  wire  0.018  inch  in 
diameter,  with  8-mil  insulation,  or  with  a  wire  0.0184 
inch  in  diameter  with  7-mil  insulation,  etc.,  the  largest 
diameter  of  copper  being  obtained  with  1.5-mil  insula- 
tion, the  diameter  of  the  wire  being  0.0208  inch. 

Therefore,  if  the  8-mil  insulation  be  used,  a  No.  25 
B.  &  S.  wire  would  be  used,  while  with  even  3-mil 
insulation  a  No.  24  B.  &  S.  wire  would  suffice,  this 
latter  wire  being  desirable. 

Likewise,  if  the  bobbin  will  contain  1.24  cubic  inches 
of  wire,  and  a  resistance  of  5000  ohms  is  required,  it  is 
evident  that  an  insulated  wire  with  4050  ohms  per 
cubic  inch  would  satisfy  this  condition,  and  by  referring 
to  Fig.  221  it  is  found  that  No.  40  B.  &  S.  wire  with 
1.5-mil  silk  insulation  will  meet  this  requirement. 

141.    RESISTANCE  CALCULATED  FROM  TURNS 

When  the  number  of  turns,  size  of  wire,  and  average 
perimeter  are  known, 

R=plpaN.  (246) 

The  size  of  insulated  wire  and  the  resistance  may  be 
determined  when  the  dimensions  of  the  winding  space 
and  number  of  turns  are  known  by  first  finding  the  value 


The  next  smaller  size  of  wire  should  be  selected 


254  SOLENOIDS 

from   the  table,  and   a   new  value  calculated   by  the 
formula  «• 

F=^-V.  (248) 

/V  ci 

The  resistance  will  then  be 

R  =  pvV.  (244) 

142.    EXACT   DIAMETER    OF    WIRE    FOR    REQUIRED 
AMPERE-T  URNS 

Since  Pi  =  ~  (249)   (see  page  228  for  values  of  <?) 
and  IN  =—  (226), 

PlPa 


d  = 


143.    WEIGHT  OF  BARE  WIRE  IN  A  WINDING 

The  weight  of  copper  in  a  winding  may  be  calculated 
from  the  activity  by  the  formula, 


(251) 

where  Wc  is  the  weight  per  unit  volume  for  bare  wire, 
i.e.  for  solid  copper. 

In  metric  measure,  1^=8.89  grams  per  cubic  centi- 
meter. 

In  English  measure,  Wc  =  0.32  pound  per  cubic  inch. 

The  weight  may  also  be  found  by  dividing  the  resist- 
ance by  the  resistance  per  unit  weight,  pw,  for  bare 
wires. 

Thus,  W*=2-.  (252) 

Pw 

Also,  Wff  =  lvWt.  (253) 


ELECTROMAGNETIC   WINDINGS  255 

144.    WEIGHT  OF  INSULATED  WIRE  IN  A  WINDING 

By  substituting  the  weight  factors  for  the  resistance 
factors,  in  any  formula,  the  weight  of  insulated  wire  in 
a  winding  may  be  obtained. 

Thus,  Wr=  (254>'  or  W'  =  VWLNa'          (255) 


wherein  WL  is  the  weight  per  unit  length. 

Wv  =  —^  (256)  =  weight  per  unit  volume  for  insulated 

d\ 
wires. 

Therefore,  Wf=  VWV.  (257) 

The  weight  may  also  be  obtained  by  dividing  the  re- 
sistance by  the  resistance  per  unit  weight. 

Thus,       Wj  =  -  (258),  or  Wf  =  —  *  .  (259) 

Pi  Pv 

Also,        W2=1WWL.  (260) 

145.     RESISTANCE    CALCULATED    FROM   VOLUME   OF 
INSULATED   WIRE 

The  resistance  may  be  calculated  from  the  weight 
values  in  Fig.  181,  or  from  the  activity,  by  comparing 
the  weight  of  a  solid  mass  of  copper  having  the  same 
volume  as  the  winding,  and  the  actual  weight  of  copper 
in  the  insulated  wire  constituting  the  winding. 

If  calculated  from  weight, 

R  =  pw  WB,  (261) 

wherein  pw  =  ohms  per  unit  of  weight  for  bare  wires. 
(See  table,  p.  308). 

If  calculated  from  activity, 

R  =  ^rVWcPw,  (262) 

wherein  Wc  =  weight  of  copper  per  unit  volume.     (See 
Fig.  181.) 


256  SOLENOIDS 

146.    DIAMETER  OF  WIRE  FOR  A  GIVEN  RESISTANCE 
To  find  the  exact  diameter  of  wire  to  use  in  a  given 
case,  when  the  increase  due  to  insulation  is  known,  use 
the  formula 


147.    INSULATION  FOR  A  GIVEN  RESISTANCE 

The  increase   due  to  insulation  may  be  determined 
for  a  special  case,  by  the  formula 


In   the    above,  c=2192xlO~8   for    metric  measure, 
and  86,284  x  10~n  in  English  measure. 


CHAPTER   XIX 
FORMS  OF  WINDINGS  AND  SPECIAL  TYPES 

148.    CIRCULAR  WINDINGS 
THE  average  perimeter  of  the  winding  is 


Pa  =  -*M,  (265) 

wherein  M  =  average  diameter  of  the  winding. 

Hence,  V=-rrMLT,                                               (266) 

wherein  T=  thickness  of  the  winding, 

and  L  =  length  of  the  winding.     (See  Fig.  190.) 


~^[   (267),    -r 

I_3 

f 



-2-1   (268),   .1.. 

<  1_ 

> 

wherein     D  = i  outside  diame-   FIG.  m- Winding  Dimensions. 

ter  of  the  winding, 

and  D1  =  diameter  of  core  4-  insulating  sleeve,  or 

true  inside  diameter  of  the  winding. 

Substituting  the  value  of  Ffrom  (266)  in  (235), 

(270) 


*±    lift  Usi 

=  -rrMLTNa.  (271) 

Then,     R  =  0. 7854  pvL(lP  -  D?)  (272) 

=  Pv7rMLT.  (273) 
From  (273)  it  follows  that 

R       xnrr-iN    =      1.273J?  (275) 

257 


258  SOLENOIDS 

Referring  to  the  charts,  pp.  314-316,  select  the 
next  smaller  size  of  wire  or  next  greater  value  for  pv 
(ohms  per  cubic  inch),  and  calculate  the  actual  diame- 
ter to  wind  to  by  the  formula 

21lE  +  D1*.  (276) 


To  find  the  internal  diameter  of  the  winding,  under 
similar  conditions,  when  the  outside  diameter  D  is 
fixed,  use  formula  derived  from  (276), 


.  (277) 

The  thickness  or  depth  of  the  winding  for  a  given 
volume  will  be, 


Substituting  —  for  Fin  (278), 
P, 


+-.  (279) 

pvirL        4          a 

By  this  method,  the  depth  of  the  winding  may  be 
calculated  for  a  standard  size  of  wire,  when  the  other 
factors  are  given. 

The  volume  of  a  winding  may  be  quickly  approxi- 
mated by  use  of  the  chart  (Fig.  191),  which  will  give 
the  value  of  TrMT,  and  then  multiplying  by  L. 

Referring  to  Fig.  191  the  winding  volume  (in  cubic 
inches)  per  inch  of  length  of  winding  is  found  by  fol- 
lowing the  curved  line,  which  starts  from  the  value  of 
Dj,  the  inside  diameter,  to  where  it  intersects  the  hori- 
zontal line  corresponding  to  the  value  of  Z>,  the  outside 
diameter,  and  then  tracing  vertically  downward. 


FORMS  OF  WINDINGS   AND  SPECIAL   TYPES       259 


As  an  example,  the  outside  of  a  winding  is  2  inches  and 
the  diameter  of  the  insulated  core,  D,  is  0.9  inch.  Follow- 
ing the  curve  which  starts  at  0.9  it  will  be  found  that  it 
intersects  the  horizontal  line  corresponding  to  2  at  the 


^ 

/ 

x 

X 

x 

^j 

JJ 

x- 

x 

xx 

x 

xt 

x 

X 

X 

x 

x^ 

x 

X 

^ 

X; 

x/j 

1 

XXf 

X1 

/7* 

x 

, 

x 

x 

x' 

x 

/ 

x 

X 

x 

x 

xx 

-X 

X 

x 

x 

x 

X 

'X 

x^ 

x^ 

<?? 

X 

/^ 

X 

x 

X 

x 

x 

x| 

x 

xx 

X 

x 

x 

x 

Xi 

x 

x 

x 

^ 

^ 

^x 

X  . 

x 

X 

x 

X 

J 

X 

x 

x 

x 

x^^ 

'Xx1 

^ 

^ 

X, 

^x 

^ 

x^j 

^x- 

x 

x 

r 

x 

x 

x 

£ 

x 

X 

^> 

x 

x 

x^ 

x 

XX 

^ 

x^ 

>  ^ 

X 

x 

X 

'  , 

x 

x 

x 

x 

x 

xx 

'x 

x 

x 

X< 

-xx^ 

x 

x^ 

X 

x 

x 

X 

xx 

/x 

^ 

X 

x 

x 

x^ 

x^ 

^ 

1 

X    > 

X' 

x 

x 

x 

x 

x 

x 

x 

/x 

x 

x 

xx^ 

x^ 

XX 

/ 

x 

X 

x^ 

/ 

^ 

x 

<x^ 

1 

XX 

/* 

> 

x/ 

^ 

</ 

x 

x 

x/l 

X^j 

XX 

x^ 

X  X. 

X 

x 

'X 

x 

x/ 

X} 

XX 

Xxj 

^J- 

xx 

x 

x 

x,, 

!// 

x 

/x 

///, 

X/ 

// 

x, 

// 

// 

2 

^ 

///; 

#' 

~7~7 

/  / 

x/ 

2 

2 

g 

^ 

~7  x 

// 

/ 

2 

^ 

^ 

75 

/ 

// 

/^ 

t// 

T^y 

// 

// 

^ 

/// 

2 

/^ 

A  2 

// 

/ 

22 

f 

/y7// 

77  y/ 

ILL 

(U- 

lf 

1 

I 

-  „  ..  c.  „  „  ,  15 '  -a  2 

WINDING  VOLUME  (CUBIC  INCHES)  PER  INCH  OF  LENGTH 

FIG.  191.  —  Chart  for  Determining  Winding  Volume. 


S       - 


vertical  line  corresponding  to  2.5  cubic  inches  per  inch  of 
length  of  winding.  If  the  length  L  be  3  inches,  the  volume 
of  the  winding  will  then  be  2.5  x  3  =  1.5  cubic  inches. 
The  superficial  area  (not  including  ends)  is 

#r=7rDZ.  (280) 

The  area  of  each  end  is  A=paT  (281),  =irMT.  (282) 


260 


SOLENOIDS 


FIG.  192.  —  Imaginary 
Square-core  Winding. 


149.  WINDINGS  ON  SQUARE  OR  RECTANGULAR  CORES 

In  the  calculation  of  windings  with  cores  of  square 
or  rectangular  cross-section,  the  form  of  the  winding  is, 
generally,  assumed  to  be  as  shown 
in  Fig.  192,  and  its  cross-sectional 
area  is  calculated  accordingly. 
That  this  method  is  very  impracti- 
cable will  be  appreciated  by  any 
engineer  who  may  have  calculated 
a  winding  by  it,  and  compared  the 
actual  characteristics  of  the  wound 
coil  with  his  theoretical  deductions. 
Most  text-books  express  the  volume  of  such  a  square- 
core  winding  by  the  formula  V=  L(IP  —  a2),  wherein 
a  and  B  are  as  in  Fig.  192,  and  L  is  the  length  of  the 
coil.  It  would  be  an  extremely  difficult  operation  to 
cause  all  the  turns  to  form  perfect  squares ;  this  would 
be  possible  only  with  exceedingly  fine  wires. 

All  practical  square-core  windings,  such  as  are  used 
on  field  magnets,  etc.,  appear  as  in  Fig.  193.     This  is 

perfectly  natural,  since  the  tension     ^^ r— ^ 

on  the  wires,  during  the  winding 

process,  tends  to  press  the  layers 

closely   together    at    the    corners ; 

hence,  the  thickness,  or  depth  T, 

of  the  winding  will  be  uniform  all 

around  the  core,  excepting  at  the    V.      i  !  ^/ 

sides,  where  it  has  a  tendency  to     FIG.   193.  —  Practical 

bulge    Outward,    Owing    to    the    re-       Square-core  Winding. 

siliency  of  the  wire,  and  the  lack  of  pressure  on  the 
flat  faces.  This  latter  effect,  however,  need  not  be 
considered  in  practice. 


•T— * 


on 


FORMS  OF  WINDINGS  AND   SPECIAL   TYPES      261 

For  a  practical  square-core  winding,  as  in  Fig.  193, 
pa  =  4  (a  +  0.7854  T).  (283) 

Assuming  T=  -,  approximately  7  per  cent  less  wire 

will  be  required  in  the  practical  type  (Fig.  193)  than 

in  the  imaginary  winding  (Fig.  192)  to  accomplish  the 

same  results  with  the  same  size  of 

core,  wire,  and  number  of  turns. 

This  is  due  to  the  decrease  in  the 

average  perimeter  of  the  winding, 

in  the  practical  type. 

As  a  matter  of  fact,  the  cores  of 
this  class  of  electromagnet  usually 
have  their  sharp  edges  rounded  off.  FlG  194.— winding 

We   may,    then,   Consider   Fig.    194         Core    between    Square 

to  be  a  fairly  accurate  representa-       aud  Round- 
tion  of  the  cross-section  of  windings  of  this  nature.     An 
inspection  of  Fig.  194  will  show  the  average  perimeter 
of  the  winding  to  be 

pa  =  7r(r+  2r)  +  2  (a  -  2r)  +  2  (5  -  2r),  (284) 
or     pa  =  2  (a  +  5)  +  TrT  -  1.717  r,  (285) 

for  windings  with  cores  of  square  or  rectangular  cross- 
section. 

Since,  for  square-core  windings,  a  =  5,  (285)  may  be 

written          pa  =  4  a  +  ^T  -  1.717r,  (286) 

or  Pa  =  4  (a  +  0.7854  T-  0.423 r).         (287) 

(287)  also  holds  for  circular  windings,  as  in  Fig.  195, 
when  a  =  2  r. 

Referring  to  Fig.  194, 

T  = 


262  SOLENOIDS 

Then,  B  =  2  T  +  a  (290),  and  B^ZT+b,     (291) 

wherein  B  and  Bl  —  outside  dimensions  of  winding. 
The  volume  of  the  winding  will  then  be 

F=  ^7^(292)=  2^(4  a  +77-^-  1.717  r)  (293) 
for  windings  on  square  cores,  or 

F  =  TL\%  (a  +  b)  +  TrT-  1.717r]       (294) 

for  windings  on  rectangular  cores. 

Substituting  the  value  of  T  from  (288)  in  (294) 

~)  [2  O  +  5)  +  W(:*=L«)-1.717  r]  (295) 


or    r=i(5-a)[(a  +  6)  +  0.7854(J?-a)  -  0.859  r], 

(296) 
for  either  square  or  rectangular  windings. 

The  following  formulae  are  here  repeated  for  conven- 
ience. By  substituting  the  values  of  pa,  T,  V,  etc.,  as 
given  above,  the  resistance,  turns,  weight,  etc.,  may  be 
readily  calculated. 

lw  =  VNa  (236),  R  =  lwPl  (239),  =  ^F 


N=  TLNa  (210),  Z^=-(226),  Pe  =     .       (245) 

PlPa  V 

For  square-core   windings,   when  the  value  of  r  is 
small  enough  to  be  neglected, 


-  + 0.406  a2 -0.6370. 
TrL 

Since  F=  -,  (298) 

Pv 


0.406  a2  -0.637  a.          (299) 
By  formula  (299)  the  thickness  of  the  winding,  for  a 


FORMS  OF  WINDINGS   AND  SPECIAL   TYPES      263 

standard  size  of  insulated  wire,  may  be  calculated  from 
the  resistance,  when  the  other  constants  are  known. 
The  superficial  area  (not  including  ends)  is 

Sr  =  2Z(0.7854  B  +  0.215  a  +  b  -  2.43  r).  (300) 
The  area  of  each  end  is  A  =  paT.  (281) 

150.    WINDINGS  ON  CORES  WHOSE  CROSS-SECTIONS 
ARE  BETWEEN  ROUND  AND  SQUARE 

In  most  cases  the  space  for  the  winding  is  of  such  a 
nature  that  its  periphery  may  be  either  a  circle  or  a 
square.  The  dimension  B  (see  Fig. 
192)  will,  therefore,  be  the  limiting 
dimension  for  either  form  of  wind- 
ing ;  consequently,  it  is  important 
to  determine  what  form  of  core  and 
winding  will  give  the  best  results 
for  any  given  case. 

In  this  particular  case  (see  Figs.      Fja  195>_RoundK;ore 
193  and  195)  the  dimension  a  repre-  Winding, 

sents  either  the  diameter  of  a  round  core,  or  one  side  of 
a  square  core. 

For  equal  areas,  the  perimeters  of  the  circle  and  the 
square  are  to  each  other  as  1  : 1.128.  Hence,  if  it  were 
possible  to  construct  a  winding  whose  thickness,  or 
depth,  would  be  zero,  the  economy  of  the  round-core 
magnet  would  be  12.8  per  cent  greater  than  that  for  the 
square-core  magnet.  However,  the  thickness  of  the 
winding  changes  the  ratio  of  average  perimeters  ;  thus, 
in  two  windings,  one  with  a  core  1  cm.  square,  and  the 
other  with  a  round  core  1  sq.  cm.  in  cross-section,  the 
thickness  of  each  winding  being  10  cm.,  the  economy 
of  the  round-core  winding  would  be  only  1.3  per  cent 


264 


SOLENOIDS 


greater  than  that  with  the  square  core.  Therefore,  for 
equal  areas,  when  T=Q,  the  round-core  winding  has 
the  maximum  economy  ;  but,  when  T7  =  oo ,  the  econo- 
mies of  the  square-core  and  the  round-core  windings 
would  be  the  same. 

The  dimension  a,  however,  will  be    12.8   per   cent 
greater   for  the  round  core  than  for  the  square  core. 


-100 


90 


FIG.  196. — Relations  between  Outside  Dimension  B  of  Square-core  Elec- 
tromagnets, and  Outside  Diameter  of  Round-core  Electromagnets. 

This  will  greatly  increase  the  outside  dimensions  of  the 
finished  coil,  where  a  round  coil  is  used ;  providing,  of 
course,  that  the  thickness  of  the  winding  is  not  great 
as  compared  with  a.  Figure  196  shows  this  relation; 
the  outside  dimension  B  being  compared,  for  equal 
core  areas  with  the  outside  diameter  of  the  round-core 
winding.  In  this  particular  case,  the  value  of  a  for 
the  square-core  winding  is  taken  in  order  to  have  the 
winding  thickness  the  same  for  both  the  square-core 
and  round-core  windings. 


FORMS   OF   WINDINGS  AND  SPECIAL   TYPES      265 

On  the  other  hand,  if  we  make  the  dimension  a  con- 
stant for  both  forms  of  cores,  and  the  thickness  of  the 
winding  equal  to  10  a,  the  average  perimeter  of  the 
square-core  winding  would  be  2.5  per  cent  greater 
than  that  for  the  round-core  winding  ;  but,  the  cross- 
sectional  area  of  the  square-core  would  be  27  per  cent 
greater  than  that  for  the  round  core. 

In  any  case  the  flux-density  per  square  centimeter  is 
expressed  by  the  formula 

(301) 


wherein  Ac  is  the  cross-sectional  area  of  the  core  in 
square  centimeters,  p  the  permeability,  I  the  current 
in  amperes,  N  the  number  of  turns  of  wire  in  the 
winding,  and  lc  the  length  of  the  magnetic  circuit. 
The  ampere-turns  are  expressed  by  equation  (226), 


PlPa 

Substituting  the  value  of  IN  horn  (226)  in  (301), 


(302) 

Assuming  the  values  of  ^,  E,  Zc,  and  pL  to  be  constant, 

^ 
the  value  of  68  will  vary  directly  with  the  ratio  —  -. 

Pa 

While  the  practical  round-core  electromagnet  has 
the  greater  economy,  magnets  with  square  cores  are, 
nevertheless,  extensively  used.  When  the  dimension 
a  of  the  core  and  the  outside  dimension  B  of  a  square- 
core  electromagnet  are  fixed,  its  economy  may  be  con- 
siderably increased  by  rounding  the  corners  of  the  core, 
as  in  Fig.  194.  It  will  be  seen  that,  by  increasing  the 
value  of  r  from  0  to  0.5  a,  the  square  core,  by  gradual 


266 


SOLENOIDS 


19 


FIG.  197.  —  Ratios  between  Round-core  and  Square-core  Electromagnets 


T 
when  -  =  0. 


10 


0  .1  .2  .3          .4  .5  .0  .7  .8  .9  1, 

FIG.  198.  — Ratios  between  Square-core  and  Round-core  Electromagnets 
when  -  =  2. 


FORMS  OF   WINDINGS   AND  SPECIAL  TYPES      267 


transition,  becomes  perfectly  round ;  a  remaining  con- 
stant. It  is,  therefore,  obvious  that,  for  various  ratios 
of  T  and  #,  the  core  and  winding,  for  maximum  econ- 
omy, will  fall  somewhere  between  the  square  core  and 
the  round  core. 
In  Fig.  197  is 
shown  the  ratios  *. 


1.5 


1.25 


,.75 


.25 


\ 


of  ^    for    flux 

Pa  A* 

density,  and  - 

for  the  total  flux, 

when    —    =    0. 
a 

Figure  198 
shows  the  rela- 

T 

tion  when— =2. 
a 

The  maximum 
values  for  6B 
and  <p  are  shown 
in  Fig.  199.  The 
values  of  p,  E,  lc  ~ 

and  p/,  as  before    FIG.  199. — Maximum  Values  for  Flux  Densities  and 
Total  Flux,  and  Ratios  between  Core  Area  and 

stated,    are    as-       Average  Perimeters. 
sumed  to  be  con- 
stant.    The  dimension  a  is  also  assumed  to  remain  con- 
stant, while  the  values  of  r  and  T  are  variable.     This 
shows  the  ratios  of  the  various  average  perimeters  and 
core  areas,  taking  the  cross-sectional  area  of  the  square 
core  as  unity  for  the  core  areas,  and  the  average  perim- 
eter of  the  square-core  winding  as  unity  for  the  average 
perimeters. 


268 


SOLENOIDS 


When  —  =  0,  a  =  B.    Hence,  the  maximum  core  area 

will  be  obtained  with  the  square  core.     The  round-core 
winding,  however,  has  the  minimum  average  perimeter, 


0    .06   .1    J.6  . 


FIG.  200.— Maximum  Flux  Density  and  Total  Flux,  for  Various  Values  of 


2r        ,    T 

-  and    — 
a  a 


and,  as  the  ratio  between  core  area  and  average  perim- 
eter is  the  same,  the  value  of  — ,  which  will  produce 

a 

the   maximum  flux    density,  will  be  found  to  be  0.5. 


FORMS  OF  WINDINGS   AND  SPECIAL   TYPES      269 

The  condition  which  shall  produce  the  maximum  flux 

is  met  when  — =  0.25. 
a 

The  proper  value  of  — -,  to  produce    maximum  re- 

a 

suits,  for  practical  windings,  will  be  found  at  the  points 
where  the  flux  density  or  the  total  flux  curves  inter- 
sect with  the  average  perimeter  curves.  This  relation 
is  shown  more  clearly  in  Fig.  200. 

The  usual  insulation  between  the  core  and  the  wind- 
ing has  not  been  considered.  However,  the  average 
perimeter  of  the  winding  may  be  compared  with  the 
total  cross-sectional  area  of  the  core,  plus  the  insulating 
medium,  and  corrections  made  for  the  difference  be- 
tween the  actual  and  assumed  core  areas.  In  any  case, 
it  is  important  that  the  average  perimeter  shall  be  cal- 
culated for  the  actual  winding  only. 

151.    OTHER  FORMS  OF  WINDINGS 

For  any  form  of  winding  volume,  simply  find  the 
average  perimeter  p^  the  thickness  of  the  winding  T, 
and  the  length  L.  From  these  dimensions  all  neces- 
sary calculations  may  be  made  by  using  the  formulse 
in  Chapter  XVIII. 

152.   FIXED  RESISTANCE  AND  TURNS 

Some  specifications  call  for  a  certain  resistance,  or 
else  the  weight  of  the  insulated  wire  is  specified. 
This  is  often  done  to  keep  a  check  on  the  manufacturer, 
to  see  that  the  full  amount  and  proper  grade  of  insu- 
lated wire  is  being  supplied.  Also,  in  certain  apparatus, 
and  particularly  that  used  in  telephone  switchboards, 
the  magnets  are  so  adjusted  that  they  will  only  operate 


270  SOLENOIDS 

above  certain  current  strengths,  and  as  these  are  con- 
nected partly  in  series  and  partly  in  multiple  in  the 
same  circuit,  with  a  fixed  voltage  operating  the  entire 
combination,  it  is  extremely  important  that  the  resist- 
ance and  turns  should  be  as  near  a  fixed  standard  as 
possible  for  each  electromagnet. 

153.   TENSION 

In  the  practical  winding  of  an  electromagnet,  the 
tension  is  a  most  important  factor,  for  if  the  wire  be 
wound  tightly  in  a  bobbin  with  fixed  winding  space, 
and  the  same  kind  of  wire  be  wound  loosely  upon 
another  identical  bobbin,  less  turns  will  be  obtained  in 
the  latter  than  in  the  former  ;  consequently  there  will 
be  less  wire  in  the  winding.  Hence,  with  voltage  con- 
stant in  both  cases,  there  will  be  less  current  consump- 
tion in  the  former  than  in  the  latter  case  for  the  same 
ampere-turns. 

It  is,  therefore,  important  to  use  a  device  which  shall 
keep  the  tension  on  the  wire  constant.  By  such  a 
means  the  tension  may  be  so  adjusted  that  all  of  the 
windings  will  be  almost  absolutely  identical  both  as  to 
turns  and  resistance. 

When  winding  fine  wires  especially,  careful  attention 
should  be  paid  to  the  tension,  not  only  as  to  uniformity, 
but  also  as  to  the  total  amount  of  tension  placed  on 
the  wire.  This  should  be  just  sufficient  to  keep  the 
wire  tight  without  stretching  it  enough  to  reduce  its 
sectional  area.  The  author  has  personally  stretched 
No.  27  wire  down  to  nearly  No.  28  by  simply  adjusting 
the  tension  on  the  winding  machine. 

Square  or  rectangular  windings  require  a  very 
strong  tension  while  being  wound,  otherwise  the  wire 


FORMS  OF   WINDINGS   AND  SPECIAL  TYPES      271 

will  not  lie  closely  on  the  flat  faces  of  the  form  or 
insulated  core.  With  the  round  or  elliptical  types, 
the  wire  naturally  tends  to  lie  close  on  account  of  the 
curvature,  as  the  wire  tends  to  take  the  shortest  path. 
It  is  thus  seen  that  the  activity  of  the  winding  will 
depend  largely  upon  the  tension. 


154.   SQUEEZING 

A  method  which  is  sometimes  resorted  to  in  practice, 
to  increase  the  activity  of  the  winding,  is  to  squeeze 
the  winding  longitudinally,  in  order  to  crowd  the  turns 
as  closely  together  as  possible.  It  will  be  remembered 
that  the  vertical  tension  is  greater  than  the  lateral. 
While  enameled  and  so-called  bare-wire  windings  can- 
not be  safely  treated  in  this  manner,  silk  and  cotton 
covered  wire  windings  may  have  their  activity  increased 
nearly  20  per  cent  in  some  cases,  without  injury  to  the 
insulation,  or  affecting  the  resistance  of  the  winding, 
the  degree  of  squeezing  being  dependent  upon  the  ratio 
of  insulation  to  copper. 

In  following  this  method  it  is  customary  to  predeter- 
mine the  amount  of  squeezing  which  may  safely  be 
applied,  and  then  calculate  the  resistance  or  turns  in 
the  usual  manner,  assuming  the  increased  length  of  the 
winding  for  L.  After  the  winding  is  formed  on  the 
bobbin  or  on  a  tube  of  insulating  material,  it  is 
squeezed  to  the  length  previously  determined. 

In  one  method  a  false  core  is  placed  end  to  end  with 
the  true  core  of  the  bobbin.  After  the  winding  has 
been  squeezed,  the  false  core  will  fall  out.  This  is  but 
one  suggestion  for  the  many  ways  in  which  this  may 
be  accomplished. 


272  SOLENOIDS 

155.   INSULATED  WIRE  WINDINGS  WITH  PAPER 
BETWEEN  THE  LAYERS 

Besides  winding  with  bare  wrire  with  a  thread  of  in- 
sulating material  between  adjacent  turns  and  paper 
between  adjacent  layers,  windings  consisting  of  regular 
insulated  wire  with  paper  between  the  layers  are  often 
used.  This  makes  a  good  winding  for  use  with  high 
voltages  or  where  there  is  a  considerable  inductance,  as 
when  used  with  alternating  currents,  since  the  entire 
winding  then  consists  of  smooth  even  layers  well  insu- 
lated from  each  other,  although  the  activity  is  greatly 
reduced. 

In  this  case  the  paper  should  project  for  varying  dis- 
tances beyond  the  winding  at  each  end  of  the  coil,  to 
prevent  a  sudden  disruptive  discharge  from  one  layer 
to  another,  around  the  edge  of  the  intervening  paper. 

For  this  type  of  winding 

d*  =  (d  +  i+8)(d  +  i  +  P).  (303) 

The  number  of  layers 

n  =  —  (304) 

(d  +  t+P) 

and  the  turns  per  unit  length 

m  =  -  —  (305) 

(d+i+-g) 

Wherein 

d  =  diameter  of  wire. 

i  =  increase  due  to  insulation. 

8  =  lateral  allowance  between  turns,  edge  to  edge. 

p  =  vertical  allowance,  or  thickness  of  paper. 

In  this  and  similar  cases,  however,  there  is  a  loss  in 
the  length  of  winding  space  varying  from  -J-  inch  for 
very  small  coils  to  1  inch  for  large  ones. 


FORMS  OF  WINDINGS   AND   SPECIAL   TYPES      273 

156.    DISK  WINDING 

While  the  disk  winding  is  not  extensively  used  on  elec- 
tromagnets, a  description  will  not  be  out  of  place  here. 

One  great  disadvantage  in  the  ordinary  method  of 
winding  electromagnets  is  in  the  fact  that  the  difference 
of  potential  between  adjacent  layers  is  liable  to  break 
down  the  insulation,  as  mentioned  in  Art.  129. 

The  disk  winding  is  designed  to  overcome  this  diffi- 
culty, and  is  wound  spirally,  like  the  mainspring  of  a 
clock  or  watch.  The  conductor  is  usually  in  the  form 
of  a  flat  ribbon,  and  is  insulated  with  silk,  cotton, 
paper,  or  other  insulating  material.  The  difference  of 
potential  between  successive  layers  is  very  slight  since 
each  layer  consists  of  but  one  turn. 

The  disks  are  then  placed  side  by  side,  connected 
together,  electrically,  and  insulated  from  each  other  by 
mica  disks.  By  this  arrangement  the  total  difference 
of  potential  is  across  the  length  of  the  winding  instead 
of  across  the  thickness  of  the  winding,  which  is  a  great 
advantage.  The  space  economy  of  this  form  of  wind- 
ing is  also  great,  as  there  are  no  interstices  between  the 
wires  outside  of  the  insulation,  as  in  the  case  of  round- 
wire  windings,  and  there  is  no  pitch  in  the  turns.  In 
this  latter  connection  the  ideal  condition  is  attained. 

Sometimes  round-wire  windings  are  made  in  the 
form  of  disks,  and  connected,  as  just  explained.  This 
is  necessary  where  fine  wire  is  used,  but  in  this  case 
the  turns  incline  toward  the  core  slightly,  as  in  the 
case  of  the  regular  round-wire  winding. 

157.   CONTINUOUS  RIBBON  WINDING 

In  what  may  be  called  a  modification  of  the  disk 
winding,  the  ribbon  is  wound  on  edge  around  the 


274  SOLENOIDS 

insulated  core,  with  suitable  insulation  placed  between 
adjacent  turns. 

This  winding  consists  of  but  one  layer,  and  is 
adapted  only  for  strong  currents.  It  is  very  efficient 
with  a  high  coefficient  of  i/r,  and  also  possesses  a  high 
coefficient  of  heat  conductivity,  owing  to  the  continuity 
of  the  copper  from  the  inside  to  the  outside  of  the  coil. 

158.   MULTIPLE- WIRE  WINDINGS 

Windings  for  various  electrical  purposes  often  consist 
of  several  wires  wound  simultaneously,  the  wires  form- 
ing  separate  circuits,  or  with  their 
terminals  connected  together  to 
act  as  one  conductor.  When  the 
wires  are  grouped  as  one  circular 
strand,  the  winding  is  more  effect- 
ive than  when  the  wires  are 
wound  on  side  by  side  in  the  form 
of  a  ribbon,  owing  to  the  greater 
FIG.  201.  — Four-wire  pitch  in  the  latter  case.  (See 

Fig.  201.) 

When  calculating  windings  of  the  class,  it  is  impor- 
tant to  use  formula  (220),  p.  286,  for  the  turns,  and 
determine  the  resistance  from  the  turns  thus  deduced. 
The  turns  and  resistance  may  be  calculated  for  each 
wire  separately,  or  the  total  resistance  may  be  deter- 
mined from  the  total  number  of  turns. 

159.    DIFFERENTIAL   WINDING 

This  winding  consists  of  two  similarly  insulated 
wires  wound  simultaneously  side  by  side.  Only  one  of 
the  wires  is  used  for  exciting  purposes,  however,  the 


FORMS   OF  WINDINGS  AND   SPECIAL  TYPES      275 

other  wire  having  its  inside  and  outside  ends  connected 
together,  thus  forming  a  closed  circuit. 

It  is  extensively  used  where  sparking,  due  to  self-in- 
ductance, is  detrimental  to  the  contacts  of  the  control- 
ling device.  When  the  circuit  of  the  exciting  winding 
is  opened,  the  short-circuited  winding  absorbs  the  mag- 
netic energy  which  would,  otherwise,  cause  a  momentary 
high  voltage  in  the  exciting  circuit. 

This  winding  is  calculated  by  the  methods  described 
in  Art.  158.  Owing  to  the  fact  that  only  one  half  of 
the  total  winding  space  is  available  for  the  exciting 
coil,  it  is  very  inefficient. 

160.  ONE  COIL  WOUND  DIRECTLY  OVER  THE  OTHER 

When  both  coils  have  the  same  size  of  insulated 
wire,  simply  calculate  as  one  coil,  making  due  allowance 
for  the  insulation  between  the  two  windings. 

When  the  sizes  of  wire  are  different,  the  coils  will,  of 
course,  have  to  be  calculated  separately,  using  the  outer 
dimension  of  the  first  coil  plus  insulation  for  the  inner 
dimension  of  the  outer  coil. 

161.  WINDING  CONSISTING   OF   Two  SIZES  OF   COP- 

PER WIRE  IN  SERIES 

It  was  stated  that  the  diameter  of  wire  calculated  for  a 
given  resistance  and  number  of  turns  in  a  fixed  winding 
space  usually  falls  between  two  standard  sizes  of  wire. 

When  a  special  diameter  of  wire  is  not  obtainable  or 
desirable,  and  the  calculated  diameter  of  wire  is  not 
sufficiently  near  a  standard  size  to  warrant  the  use 
of  the  latter,  two  wires  may  be  employed,  the  average 
resistance  and  turns  of  which  will  be  approximately  as 
desired. 


276  SOLENOIDS 

Since  the  number  of  turns  will  be  inversely  propor- 
tional to  the  difference  between  the  required  resistance 
and  the  resistance  which  would  be  obtained  by  using 
the  adjacent  sizes, 


r  v  max          Pv  min 

and  N 


PV  max          Pvnrin 

where        JVX  =  number  of  turns  of  smaller  wire, 
and  .ZVjj  =  number  of  turns  of  larger  wire. 

Then,  N=lT1+Ny  (308) 

The  thickness  or  depth  of  the  winding  for  each  size 
of  wire  will  be 

-  pv  cal)  ^  (309) 


PO  max          P 


Pv  max          Pv  min 

where  T^  =  thickness  of  smaller  wire  winding, 
and      T2  =  thickness  of  larger  wire  winding. 

Then,  T=Tl+T(,.  (311) 

As  the  smaller  winding  will  have  the  greater  loss  in 
watts,  and  therefore  become  the  hotter  of  the  two,  it  is 
customary  to  place  it  over  the  larger  wire  winding. 

It  is  then  only  necessary  to  determine  the  value  of 
the  average  perimeter  pa,  for  each  winding,  to  calculate 
the  resistance,  the  length  of  the  winding  being  constant. 

Sometimes  it  is  required  to  obtain  a  high  resistance 
in  an  electromagnetic  winding  which  has  so  small  a 
winding  space  that  even  No.  40  copper  wire  will  not 


FORMS   OF  WINDINGS  AND   SPECIAL  TYPES      277 

produce  the  required  resistance.  In  such  cases  the 
smallest  available  copper  wire  should  be  used,  the 
balance  of  the  resistance  being  obtained  with  some 
resistance  wire.  The  above  method  is  applicable  to 
this  case. 

162.   RESISTANCE  COILS 

These  are  calculated  after  the  same  manner  as  electro- 
magnetic windings  consisting  of  copper  wire,  but  the 
resistance  will  vary  in  direct  proportion  to  the  relative 
resistances  of  copper  and  resistance  wire.  Thus,  if  a 
winding  is  to  contain  10,000  ohms  of  Climax  wire, 
divide  by  50  and  calculate  the  same  as  though  the  coil 
was  to  consist  of  copper;  that  is,  the  same  as  if  the 

T     10,000      OAfk    , 

resistance  was  to  be  — — —  =  200  ohms,  using  the  regu- 
«50 

lar  copper  wire  charts. 

Resistance  coils  are  usually  wound  Non-inductively ; 
that  is,  two  wires  are  connected  together,  the  joint  being 
thoroughly  insulated,  and  fastened  to  one  of  the  heads 
of  the  spool,  and  then  the  two  wires  are  wound  on  to- 
gether in  parallel.  Both  wires,  therefore,  have  the  same 
number  of  turns  and  the  current  flows  toward  the  inner 
connection  in  an  opposite  direction  to  which  it  flows  out, 
thus  neutralizing  any  magnetic  tendency,  and  eliminat- 
ing the  inductive  effects. 

163.    MULTIPLE-COIL  WINDINGS 

Among  the  several  methods  of  winding  electromag- 
nets so  that  the  sparking  due  to  self-induction  shall  be 
minimized,  the  best  two  are  what  are  known  as  the  Dif- 
ferential winding  and  the  Multiple-coil  winding.  This 
does  not  refer  to  external  methods  of  compensation. 


278 


SOLENOIDS 


The  differential  winding  is  less  expensive  than  the 
multiple-coil  winding,  for  a  given  voltage,  as  much 
coarser  wire  and  less  turns  are  used  in  the  former 
than  in  the  latter. 

The  extreme  commercial  condition  for  the  multiple- 
coil  winding  is  illustrated  in  Fig.  202,  where  the 

respective  ends  of 
each  layer  are  all 
connected  together. 
Since  in  this  type  of 
winding  the  full  volt- 
age is  across  each  of 
the  multiple  wires  or 
separate  coils,  this 
arrangement  is  not 

Fio.  202.- Winding  with  Layers  connecsted  practicable  for  corn- 
in  Multiple,  paratively  high  volt- 
ages on  coils  of  moderate  size,  as  the  wire  in  each  layer 
would  have  to  resist  the  full-line  voltage  without  over- 
heating. This  applies  most  fully  to  the  first  or  inner 
coil,  which,  having  the  least  resistance,  must  pass  the 
most  current. 

The  principle  of  the  multiple-coil  winding  is  that  the 
inner  turns  (or  separate  coils)  have  less  resistance  but 
a  greater  coefficient  of  self-induction  than  the  outer  turns, 
owing  to  the  different  diameters  of  the  inner  and  outer 
turns,  and  hence  the  time-constants  of  the  separate 
windings  are  different. 

For  electromagnets  three  or  four  inches  in  length  by 
two  or  three  inches  in  diameter,  to  operate  on  110-volt, 
direct-current  circuit,  the  author  has  had  excellent 
results  from  six  separate  windings  per  spool,  wound 
over  each  other,  and  connected  in  multiple,  as  in  Fig. 


FORMS  OF  WINDINGS  AND  SPECIAL   TYPES      279 


203.     While  Fig.  203  shows  the  terminals  at  opposite 
ends  of  the  bobbin,  by  making  the  layers  even  in  num- 


INSIDE 


OUTSIDE  ENDS 


FIG.  203.— Practical  Multiple-coil  Winding. 

ber,  the  terminals  may  be  brought  out  at  the  same  end 
of  the  winding,  as  in  Fig.  204.  This  arrangement  pro- 
duces the  same  general  effect  as  six  layers  of  coarser 
wire,  with  a  corresponding  decrease  in  voltage,  and, 
therefore,  is  just  as  efficient,  with  the  exception  that 
there  will  be  less  copper  in  the  fine-wire  winding, 
owing  to  the  greater  ratio  of  insulating  material  on  the 
fine  wire. 

In  order  to  ascertain  the  safe  current  carrying  capac- 
ity of  the  winding,  a  plain  or  regular  winding  may  be 
assumed.  As  an  ex- 
ample consider  the 
bobbin  in  Fig.  205. 
The  winding  is  to  be 
connected  directly 
across  110  volts  di- 
rect current,  and  will 

be  in  Use  at  Such  in-  FIG.  204.  — Method  of  bringing  out 

Terminals. 


tervals     that     13.75 

watts  will  be  permissible  for  the  winding. 

ance  of  the  winding  will  then  be 


The  resist- 


12,100 

-j_ 


880  ohms. 


280  SOLENOIDS 

Referring   to  Fig.  206,  M  is  the  mean  or   average 
diameter  of  the   entire    winding   space,  and   Ma,   Mb, 

"f     etc.,   are    the   average 
____  ;       diameters  of  the  coils 

-'  :^      constituting  the    mul- 

_________  j  _____   .__]  U       ?*     tiple-coil     winding. 

Therefore,      M     also 
—  i  -    represents  the  average 
of  the  mean  diameters 


FIG.  205.  -Bobbin.  of  the  coils  a,  b,  c,  etc. 

If  all  the  coils  were  of  the  same  diameter,  and  hence 
of  the  same  resistance,  the  joint  resistance  would 

M 
be  proportional  to  —  ,  where  n  is  the  number  of  coils, 

n 

6  in  this  case. 

Although    the   mean    diameters    Ma,    Mb,    etc.,    are 
variable,  they  vary  in  a  direct  ratio  to  one  another, 

and  therefore  by  comparing  -  of  their  "  average  mean 

n 

diameter  "  with  their  "  joint  mean  diameter,"  we  may 
obtain  a  basis  from  which  to  compute  the  proper  wire 
to  use  which  shall  give  the  desired  resistance  when  the 

coils  are  connected  in  multiple.     -  of  the  average  mean 

n 

diameter  =  —  =  14^  =  .292  =  Ma  (see  Fig.  206).     The 
n          b 

joint  mean  diameter  will  be 

*'-  *  <313> 


=  — ^-=.  274. 


.889  +  .727  +  .615  +  .533  +  .471  +  .421     3.656 


FORMS  OF   WINDINGS  AND  SPECIAL   TYPES      281 


Therefore,    the    ratio    will    be    .274  :  .292=  .94: 1, 
which  means  that  the  joint  resistance  will  be  .94  times 


1.25 
1.2 

l.i 

1.1 

i' 

£  •' 

!•• 

•S   5 

J 

f 

-e 

+s 

-j- 

H 

c 

I 

f 

x^ 

i 

d 

M, 

1 

£ 

li^ 
^Md 

=*- 

£ 

l^ 

5 

4- 

^ 

P 

-b- 

3- 

^ 

x- 

Mb 

a 

? 

f 

x^ 

^M 

x^ 

^ 

^x 

[x' 

s" 

x***' 

xx 

^x 

^X 

•^ 

FIG.  200.  — Mean  Diameters  of  Multiple-coil  Windings. 

-  of  the  average  resistance  of  the  coils,  and  since  the 
n 

latter  is 

T?        Ra  +  RI>  H 
-K>A  =  - 


n? 


the  joint  resistance 


R, 


(314) 
(315) 


e  +  Rf) 


and  since  72;  =  880  and  n  =  6, 
(Ea  +  Rb  +  Rc+Rd+  Re 


36 


=  33,700. 


33  700 
Therefore,  the  ohms   per  cubic  inch  =      '        =  2335, 

which  corresponds  very  nearly  to  No.  39  B.  &  S.  wire 
with  2-mil  insulation. 


282  SOLENOIDS 

If  paper  is  inserted  between  the  coils,  and  an  insulat- 
ing varnish  used,  a  No.  39  B.  &  S.  wire  with  1.5-mil 
silk  insulation  would  meet  this  requirement.  There- 
fore, assuming  the  ohms  per  cubic  inch  to  be  2335,  and 
calculating  the  volumes  of  the  coils  separately,  which 
are  found  to  be  1.55,  1.89,  2.23,  2.58,  2.92,  and  3.26  cubic 
inches,  respectively,  the  resistances  will  be  3620,  4410, 
5210,  6020,  6820,  and  7610  ohms,  respectively.  Their 
joint  resistance  will  then  be: 

_  !_  __ 

3  6^  0  +  WlO"  +  WTO"  +  6  oVo  +  6  sW  + 


.000276  +  .000226  +  .000192  +  .000166  +  .000147 

+  .000131 

=880. 


.001138 
Now  also  the 


.  M} 
- 


Ma     TM\      M 

\n  J 

i — i — r^i — i — TV       (316) 

and  since  (Ea  +  Rb  +  Rc  +  Rd  +  Re  +  Rf)  =  Es,     (317) 
R.  = ^ x  ^ 

^  /^   1  1  *1~I1\          /v»2 


(318) 


and  hence 


FORMS  OF   WINDINGS  AND  SPECIAL  TYPES      283 

Therefore,  to  calculate  the  ohms  per  cubic  inch,  pv, 
direct,  use  the  formula 


Pv  — 


where  V  is  the  total  volume  of  the  winding  space  in 
cubic  inches. 

In  practice,  paper  or  other  insulating  material  is 
placed  between  the  separate  coils,  since  the  total 
voltage  is  between  adjacent  coils,  and  hence  the  space 
occupied  by  the  paper  or  other  insulating  material  must 
be  deducted  from  the  total  winding  volume.  It  will  be 
observed  that  the  resistance  of  the  inner  coil  a  is  only 
3620  ohms,  while  that  of  the  outer  coil  /  is  7610 
ohms,  which  is  more  than  twice  the  resistance  of  coil  a. 
Therefore,  there  will  be  generated  in  the  inner  coil  a 
twice  as  much  heat  as  generated  in  the  outer  coil, 
and  hence  if  the  proper  resistance  is  not  provided, 
coil  a  will  get  very  hot  unless  there  is  a  sufficient  mass 
of  core  material  to  conduct  away  the  heat  to  be  radiated 
from  the  frame. 

Instead  of  calculating  the  "  ohms  per  cubic  inch  "  for 
the  wire  used  in  the  multiple-coil  winding,  a  regular 
winding  of  one  coil  may  be  assumed,  and  the  diameter 
of  the  wire,  found  by  comparing  the  ohms  per  cubic 
inch  with  the  diameter  of  the  wire  in  Figs.  216  to  221. 

The  diameter  of  the  wire  for  the  multiple-coil  wind- 
ing will  then  be 

(321) 


wherein  n  is  the  number  of  coils. 


284  SOLENOIDS 

As  this  is  only  an  approximate  method,  it  is  best  to 
assume  4-mil  insulation  for  the  regular  winding,  and 
2-mil  or  1.5-mil  insulation  for  the  multiple-coil  wind- 
ing. To  determine  the  proper  size  of  wire  (4-mil  increase 
insulation  in  this  case)  the  ohms  per  cubic  inch  must 
now  be  found,  which  of  course  are  equal  to  the  resistance 
divided  by  the  volume  of  the  winding  in  cubic  inches. 

The  volume  of  the  winding  will  be  irMLT.  In  the 
case  considered 

•       F- s.1416  x  f?itn  x  8.6 


2 
3.1416  x  1.75  x  3.5  x  .75  =  14.43  cubic  inches,  and  the 

880 

ohms  per  cubic  inch  will  be  —  •—  =  61.     A  glance  at 

14.43 

Fig.  219  shows  that  the  nearest  B.  &  S.  copper  wire 
with  4-mil  insulation  is  No.  31. 

Formula  (321)  is  derived  from  the  fact  that  in  any 
case  the  resistance  per  unit  volume  for  any  wire  is  in- 
versely proportional  to  the  fourth  power  of  the  diameter 
of  the  wire.  (The  presence  of  the  insulation  varies 
this  somewhat,  so  formula  (321)  is  only  approximate.) 

c?4 


And  since   Rt  =  nzR  (approximately),  d*  =  -%,  where 
d  =•-— 


164.  RELATION  BETWEEN  ONE  COIL  OF  LARGE 
DIAMETER  AND  Two  COILS  OF  SMALLER  DIAMETER, 
SAME  AMOUNT  OF  INSULATED  WIRE  WITH  SAME 
DIAMETER  AND  LENGTH  OF  CORE  IN  EACH  CASE 

In  order  to  make  the  relation  clear  assume  an  actual 
example  :  In  both  cases  assume  J  inch  diameter  cores  of 
the  same  length.  Assume  the  diameter  of  the  insulating 


FORMS  OF   WINDINGS   AND  SPECIAL   TYPES      285 

sleeve  D1  to  be  .55  inch,  and  the  length  of  the  winding 
L  to  be  2  inches  in  each  case.  The  total  resistance  in 
each  case  will  be  100  ohms,  the  wire  No.  28  S.  S.  C. 
(/op  =  19.5),  and  the  e.  m.  f.,  say  50  volts. 

Case  1.     One  coil  only,  of  100  ohms. 

By  formula  (276), 


.273 


From  (267),          M=  l  =  1.22. 

4 

Therefore,  pa  =  wM=  3.83,  and  from  (226) 

1N=  —  =  2420. 
PiP* 

Case  2.     Two  coils  of  50  ohms  each. 


1.27312 


From  (276)  D  =  \-         -  f  D*=  Vl.93  =  1.39. 


From  (267)  M  =          D\  =  .97.     Therefore,    ^  =  3.04. 

A 

In  this  case  ^=25  for  each   coil.      Therefore,   IN— 

T1 

-  =  1525  for  each  coil,  or  3050  ampere-turns  for  two 

PiP« 

coils,  making  an  increase  of  26  per  cent  for  case  2  over 

case  1,  with  the  same  kind  and  amount  of  insulated  wire 

in  each  case. 

165.   DIFFERENT  SIZES  OF  WINDINGS  CONNECTED  IN 

SEKIES 

When  two  windings  of  different  volumes  are  to  be 
connected  in  series,  each  being  wound  with  the  same 
size  of  wire,  and  with  a  fixed  total  resistance,  it  is 
customary  to  proceed  as  follows; 


286  SOLENOIDS 

EXAMPLE:  Two  windings,  when  connected  in  series, 
are  to  have  a  total  resistance  of  50  ohms.  Their  rela- 
tive volumes  are  as  1  :  6.  What  should  be  the  resistance 
of  each  ? 

SOLUTION:  Let  ^  =  resistance  of  first  winding. 

J^2  =  resistance  of  second  winding. 

^  +  ^2=50,    and    since    6^  =  ^,    6^  +  ^  =  50, 
whence,    7^  =  50,   or    7^  =  7.143.     Since   E2 


166.    SERIES  AND  PARALLEL  CONNECTIONS 

When  several  electromagnets  are  to  be  operated 
simultaneously,  they  may  be  connected  in  two  different 
ways  ;  that  is,  in  series  or  in  parallel.  The  former 
method  is  the  cheaper,  as  coarser  wires  may  be  used 
in  the  winding.  The  total  current  consumption,  how- 
ever, will  be  about  the  same  in  both  cases.  The  mul- 
tiple arrangement  is  the  safer,  however,  as  any  of  the 
connections  to  the  electromagnet  may  be  broken  with- 
out affecting  the  rest  of  the  electromagnets  in  the  line, 
while  if  any  of  the  connections  should  become  broken 
in  the  series  arrangement,  the  entire  circuit  would  be- 
come inoperative.  On  the  other  hand,  there  is  more 
danger  from  short-circuits  in  the  multiple  than  in  the 
series  arrangement. 

Where  the  electromagnets  are  connected  in  series, 
the  total  line  current  passes  through  all  of  the  wind- 
ings, while  each  winding  consumes  but  a  portion  of  the 
total  voltage,  whereas,  in  the  multiple  arrangement, 
the  total  line  voltage  is  across  the  terminals  of  each 
winding,  while  each  winding  consumes  but  a  portion 
of  the  total  current  ;  therefore,  the  multiple  arrange- 


FORMS  OF   WINDINGS  AND   SPECIAL  TYPES      287 

ment  requires  much  finer  wire  in  the  windings  of  the 
electromagnets.  The  cost  of  operating,  however,  will 
be  about  the  same  in  both  cases,  as  the  only  variation 
will  be  in  the  relation  of  insulation  to  copper  in  the 
finer  or  coarser  insulated  wires.  The  above  holds  true 
where  the  line  has  a  negligible  resistance. 

167.   WINDING  IN  SERIES  WITH  RESISTANCE 

There  are  many  cases  in  practice  where  an  electro- 
magnet is  operated  in  a  circuit  containing  a  resistance 
in  series  with,  and  external  to,  the  resistance  of  the 
winding  itself.  Theoretically  there  will  always  be 
some  external  resistance,  as,  for  instance,  the  resist- 
ance of  the  leads  to  the  electromagnet  and  other  wir- 
ing ;  but  since  the  resistance  of  the  windings  for  local 
use,  and  particularly  if  designed  to  remain  in  circuit 
indefinitely  without  overheating,  is  great  as  compared 
with  the  resistance  of  the  wiring  and  source  of  energy, 
this  external  resistance  is  not  usually  considered. 

However,  in  this  article  the  resistance  in  the  circuit 
external  to  the  resistance  of  the  winding  will  be  taken 
into  consideration.  The  old  rule  "Make  the  internal 
and  external  resistances  equal "  holds  for  the  maxi- 
mum electrical  power  in  watts  which  may  be  obtained 
in  a  winding,  and  also  for  the  maximum  magnetizing 
force  for  the  winding  under  certain  conditions  ;  but 
this  rule  is  not  strictly  correct  as  applied  to  the  con- 
ditions in  actual  practice.  Under  these  conditions  the 
winding  of  the  magnet  should  have  slightly  less  resist- 
ance than  the  line,  in  order  to  do  the  most  work,  pro- 
viding, of  course,  that  the  winding  volume  is  great 
enough  to  prevent  the  winding  from  becoming  over- 
heated. 


288 


SOLENOIDS 


With  fixed  winding  volume,  the  activity  will  vary 
with  the  size  of  the  insulated  wire.  Hence,  if  the  resist- 
ance of  the  winding  be  increased,  the  activity  will  be 
decreased. 

If  we  let  E  —  voltage  of  source  of  energy, 
El=  voltage  across  winding, 
R  =  resistance  of  winding, 
and  Rl  =  all  other  resistance  in  the  circuit, 

then  =  (822) 


FIG.  207.  —  Characteristics  of  Two  Resistances  in  Series. 

Figure  207  shows  the  percentage  of  maximum  values 
for  volts  and  watts  for  the  winding  according  to  this 
rule,  the  watts  being  maximum  when 

— 


and  U  =  — 


Now  consider  a  magnet  winding  of  fixed  dimensions 
in  series  with  an  external  resistance,  equal  to  that  of 
the  magnet  winding,  and  a  source  of  energy  of  con- 

x72 

stant  voltage.     When  —  -  =  1,  which  would  be  the  ideal 


FORMS  OF  WINDINGS  AND   SPECIAL   TYPES      289 

condition  for  round  wire,  the  ampere-turns  will  attain 
their  maximum  value  for  that  size  of  wire,  but  if,  as 
in  the  case  of  a  No.  30  wire  insulated  with  4-mil  in- 

70  \ 

—  =  0.51  \  it  would  be  necessary  to 


use  a  wire  of  approximately  twice  the  resistance  per 
unit  length  in  order  to  keep  the  resistance  of  the  mag- 
net winding  the  same  in  the  latter  case  as  in  the  former, 
and  hence  when  the  watts  in  the  magnet  winding  were 
maximum,  the  ampere-turns  would  be  approximately 
50  per  cent  of  their  maximum  value  for  ampere-turns 
in  the  ideal  case. 

However,  there  are  two  distinct  effects  to  be  con- 
sidered :  (a)  in  which  case  the  space  occupied  by  the 
insulation  on  the  wire  bears  a  constant  relation  to  the 
space  occupied  by  the  wire  throughout  the  various 
sizes  of  wire,  and  (5)  in  which  the  thickness  of  insu- 
lating material  on  the  wire  is  constant  for  all  the  vari- 
ous sizes  of  wire.  In  the  former  case  (&)  it  would  be 
necessary  to  use  a  different  thickness  of  insulating 

JO 

material  for  each  size  of  wire,  in  order  to  keep  —  con- 

di 
stant,  and  hence,  case  (6)  is  the  method  adopted   in 

practice.     In  this  latter  case  the  value  of  —  changes 

<*l 
with  every  change  in  the  size  of  the  wire. 

By  assuming  E  =  100  and  Rl  =  100,  the  relations 
in  Figs.  208  to  210  have  been  calculated.  Under 
these  conditions  the  maximum  value  for  the  watts  in 
the  winding  will  be  25,  when  El  =  50  and  R  —  100. 

d2 

Figure  208  shows  the  relations  for  several  values  of  — 

dl 

under  case  (a)  in  which  these  values  are  constant.     It 


290 


SOLENOIDS 


will  "be  noted  that  the  ampere-turns  and  watts  are 
maximum  simultaneously  for  each  respective  value 

J2 

of  — ,  and  that  this  point  is  determined  by  the  inter- 

fn 

section  of  the  volts  curve  with  the  ordinate  0.5. 
While  the  maximum  value  for  watts  is  25  for  any  size 
of  wire,  under  these  conditions,  the  ampere -turns  vary 
in  the  ratio  shown  in  Fig.  209. 


20    21    22    23 


25    26     27    28    29     30   31    32    33    34    35    36 
Sizes  of  Wires.  B.<fc-S.(3auge 


FIG.  208.  —  Effect  with  Variable  Thickness  of  Insulation,  ^  Constant. 

In  Figs.  208  and  209  the  relations  expressed  by  the 
rule  first  referred  to  hold  true,  but  in  Fig.  210,  where 

the  values  of  — -  are  variable  (case  5),  the  watts  and 

ampere-turns  are  not  maximum  simultaneously, 
although  the  point  of  maximum  watts  is  deter- 
mined by  the  intersection  of  the  volts  curve  with  the 
ordinate  0.5,  as  in  case  (a), -Fig.  208. 

?2 

The  point  for  maximum  ampere-turns  with  —  varia- 
ble (Fig.  210)  is  determined  by  the  intersection  of  the 
insulation  curve  with  the  ampere-turns  curve  for  that 


FORMS  OF   WINDINGS  AND  SPECIAL   TYPES      291 


TO 

insulation.     This   gives   the   value   of  —  which   will 

V 
show   the    percentage    of    ideal    ampere-turns,   as    in 

Fig.    209.       This   curve   is    reproduced    in    Fig.    210 
(marked  e),  and  its  origin  is  at  the  intersection  of  the 


100 
90 
80 
70 

I" 

§60 

I 

40 
80 
20 

10 
0 

\ 

10 

i 

V 

~^ 

.6 

V 

\ 

JL 

d] 

Values 

X3 

\ 

\| 

J 

>» 

28 


29  SO  31  32  83 

Size  of  Wire.  B.&  S. Gauge 


FIG.  209.  — Effect  of  Insulation. 

ideal  volts  curve  and  the  ordinate  0.5,  which  ordinate 
represents  the  maximum  value  for  the  percentage  of 
ideal  IN  (curve  e). 

The  size  of  wire  which  will  give  the  maximum 
ampere-turns  under  these  conditions,  and  with  a  given 
thickness  of  insulation,  is  determined  by  the  intersec- 


292 


SOLENOIDS 


tion  of  the  volts  curve  for  the  given  insulation  with 
curve  e.  Having  once  plotted  curve  e,  it  is  an  easy 
matter  to  find  the  size  of  wire  to  give  the  maximum 
ampere-turns  for  any  case,  by  first  calculating  the  size 
of  wire  (assuming  the  insulation  to  be  nil)  which 
will  produce  the  maximum  ampere-turns  for  the  ideal 

/  70  \ 

case  ( — -  =  1  j.     Two  points  for  volts  may  then  be  cal- 
V*l          / 

culated,  taking  into  consideration  the  insulation  on  the 


23    24    25    28    27     28     29    80     31 
Size  of  Wire.  B.&  S. Gauge 


33    84    85    90 


Fia.  210.  — Effect  with  Constant  Thickness  of  Insulation,  — ^  Variable. 

wire.  One  of  these  points  should  be  taken  on  the 
ordinate  0.5,  i.e.  when  R=R±  I  and  hence,  El  =  —  J, 

calculating  the  size  of  the  wire.  The  other  point 
should  be  taken  for  voltage  on  the  abscissa  represent- 
ing the  size  of  wire  to  produce  ideal  ampere-turns,  re- 
ferred to  above.  Connecting  these  points  will  locate 
the  size  of  wire  on  curve  e,  which  will  produce  the 
maximum  ampere-turns  with  the  given  insulation  as 
previously  explained. 

Figure  211  shows  this  principle,  in  which  curve  e  is 


FORMS   OF   WINDINGS   AND   SPECIAL   TYPES      293 


plotted  to  the  same  scale  as  in  Fig.  210.  In  this  case, 
however,  the  curve  is  a  straight  line  at  an  angle  of 
50°  with  the  ordinate  0.5. 

As  an  example,  assume  a  solenoid  with  an  available 
winding  volume  of  20  cubic  inches,  and  with  an  average 
diameter  of  2  inches  to  be  operated  on  a  220-volt  cir- 
cuit, in  series  with  a  resistance  of  200  ohms.  Assum- 

79 

ing  —  =  l^  and  by  rearranging  (263),  the  diameter  of 

the  wire  is  found  to  be  0.017  inch,  or  between  Nos.  25 
and  26  (approximately  No. 
25.4)  B.  &  S.  By  (226),  or 
referring  to  Fig.  188,  p.  247, 
the  ampere-turns  are  found  to 
be  approximately  5850.  Now 
when  E  =  EV  R  —  Ev  and 
hence  the  resistance  of  the 
solenoid,  when  watts  are  maxi- 
mum, will  be  200  ohms.  As- 
suming 8-mil  insulation,  and 
calculating  d  from  (263),  the 
diameter  of  the  wire  is  found 
to  be  0.0136  inch,  or  between 

TsTn^     97  ami   98    nr   Iw  formula  2&          26         27         28         29 

IN  Ob.   li    ana  ^O,0      Oy   3  SUe  of  Wire  B.&S..  Gauge 

(190),    the   fractional    size    is     FIG.  211.  —  Curve  "e"  as  a 
found  to  be  very  near  No.  27.5.  Straight  Line. 

The  point  where  the  voltage  curve  intersects  the 
ideal  abscissa  is  calculated  from  the  same  size  of  wire 
as  in  the  ideal  case,  i.e.  No.  25.4  or  0.017  inch  diameter, 
but  with  8-mil  insulation.  By  (273)  the  resistance  is 
found  to  be  95.5  ohms,  and  by  (322)  the  voltage  El 
is  71,  or  32.2  per  cent  of  220  volts.  Therefore  the 
size  of  wire  with  8-mil  insulation,  which  will  produce 


1 
if 

to 

8-Mil.  IDB. 

: 

2 

00 

5 

1 

i 

2 

^ 

\ 

L^ 

7 

/ 

'\ 

i 

j 

i 

294  SOLENOIDS 

the  maximum  ampere-turns  under  these  conditions,  is 
approximately  No.  26^. 

As  a  practical  proposition,  the  size  of  wire  may  be 
calculated  for  a  50  per  cent  drop  in  volts  across  the 
winding,  using  the  next  larger  size  of  wire,  unless  the 

TfO 

value  of  —  is  near  unity.     Therefore,  calculate  the  size 

a1 

of  wire  to  use,  assuming  the  resistance  of  the  coil  to  be 
equal  to  the  total  external  resistance,  and  then  try  the 
next  larger  size  of  wire,  selecting  that  which  gives  the 
greatest  number  of  ampere-turns. 

NOW  ^i 

R 


Substituting  the  value  of  R  from  (322)  in  (323), 


E  d% 

The    ampere-turns    are    maximum    when    —  J  —     is 


maxmum. 
Therefore, 


IN  =  /p  .,  ,      2X  -  .          (325) 
Rdi\     cpa 


TL  d* 


168.   EFFECT  OF  POLARIZING  BATTERY 

When  a  battery  is  to  be  used  for  continuously  and 
interruptedly  operating  an  electromagnet  of  low  elec- 
trical resistance,  a  non-polarizing  type  of  battery,  pref- 
erably a  storage  battery,  should  be  used. 


FORMS  OF   WINDINGS  AND  SPECIAL   TYPES      295 

If,  however,  the  electromagnet  is  of  the  horseshoe 
or  plunger  type,  where  very  little  current  is  required 
to  maintain  the  required  pull  near  the  cores,  and  the 
operating  current  is  to  be  left  011  for  a  considerable 
period  of  time,  it  is  sometimes  desirable  to  use  a  polar- 
izing primary  battery;  as  the  current  will  fall  off 
rapidly  after  the  electromagnet  has  performed  its  duty, 
and,  therefore,  the  winding  will  not  become  so  heated 
as  it  would  if  the  full  strength  of  the  battery  current 
should  pass  through  the  winding.  There  will  also  be 
a  saving  in  energy,  thus  prolonging  the  life  of  the 
battery. 

This  arrangement  also  permits  of  a  smaller  electro- 
magnet being  used  than  if  the  operating  current  were 
to  be  left  on  the  winding  continuously,  thus  saving  in 
first  cost  also. 

169.    GENERAL  PRECAUTIONS 

The  success  of  accurately  calculating  electromagnetic 
windings  depends  upon  close  attention  to  details.  The 
wire  should  always  be  carefully  gauged  in  several  places 
with  a  ratchet-stop  micrometer,  allowances  being  made 
for  very  small  variations  in  the  diameter.  The  di- 
ameter over  the  insulation  should  also  be  carefully 
observed. 

The  winding  volume  should  be  accurately  deter- 
mined, and  the  insertion  of  paper  into  the  winding 
avoided  as  much  as  possible.  The  tension  should  be 
constant  and  not  great  enough  to  stretch  the  wire. 
The  turns  and  resistance  should  be  carefully  compared, 
as  this  will  aid  in  detecting  any  irregularities  in  the 
winding. 


CHAPTER   XX 

HEATING  OF   ELECTROMAGNETIC  WINDINGS 
170.    HEAT  UNITS 

THE  C.  G.  S.  unit  of  heat  is  the  Calorie,  and  is  the 
quantity  of  heat  required  to  raise  the  temperature  of 
one  gram  of  water  one  degree  C.  at  or  near  its  tem- 
perature of  maximum  density  4°  C. 

The  Mechanical  Equivalent  is  4.16  x  107  ergs. 

The  unit  of  heat,  in  English  measure,  is  the  British 
Thermal  Unit,  abbreviated  B.  T.  U.,  and  is  the  quantity 
of  heat  which  will  raise  the  temperature  of  one  pound 
of  water  one  degree  F.  at  or  near  its  temperature  of 
maximum  density,  39.1°  F. 

The  mechanical  equivalent  was  found  by  Joule  to 
be  772  foot-pounds.  Thus  772  foot-pounds  is  called 
Joule  8  Equivalent.  Professor  Rowland,  however,  found 
the  equivalent  to  be  778  foot-pounds.  Hence,  1  B.  T.  U. 
=  778  foot-pounds. 

1  foot-pound  =  —  =  0.001285  B.  T.  U. 

778 

One  calorie  =  0.00396  B.T.U.;  1  B.T.U.  =  251.9 
calories. 

The  electrical  unit  of  heat  is  the  Joule  or  Watt-second, 
and  is  the  quantity  of  heat  generated  in  one  second  by 
one  watt  of  energy.  One  joule  =  107  ergs. 

171.    SPECIFIC  HEAT 

The  Specific  Heat  of  a  body  at  any  temperature  is  the 
ratio  of  the  quantity  of  heat  required  to  raise  the  tern- 


HEATING  OF   ELECTROMAGNETIC   WINDINGS      297 


perature  of  the  body  one  degree,  to  the  quantity  of 
heat  required  to  raise  an  equal  mass  of  water  at  or 
near  its  temperature  of  maximum  density,  through  one 
degree. 

The  specific  heat  of  copper  at  50°  C.  or  122°  F.  is 
0.0923,  and  for  German  silver,  at  the  same  temperature, 
0.0947. 

172.    THERMOMETER  SCALES 

The  standard  thermometer  scales  in  common  use  are 
the  Fahrenheit  and  Centigrade.  In  the  former,  the  tern- 


90 
SO 
?0 
60 
SO 
40 

30 
20 
10 


2O 


6>O          8O  /OO  I2O          14O          /6O         /80          20O 


FIG.  212.  —  Comparison  of  Thermometer  Scales. 


298  SOLENOIDS 

perature  of  melting  ice  is  marked  32°  and  the  tempera- 
ture of  boiling  water  212°.  The  centigrade  scale, 
invented  by  Calcius,  is  divided  into  100  equal  parts 
between  0°  for  the  freezing  point,  and  100°  for  the 
boiling  point ;  hence  its  name.  In  both,  the  scales  are 
projected  as  far  above  the  boiling  point  or  below  the 
freezing  point,  as  may  be  desired.  The  centigrade 
scale  is  preferable. 

Conversion  from  one  scale  to  the  other  may  be 
accomplished  by  means  of  the  following  formulae: 

_F°  =  f<7°  +  32.  (326) 

0°=  |(lTO-32).  (327) 

Figure  212  also  shows  the  relations. 

The  full  line  shows  the  scale  relations,  while  the 
dotted  line  shows  the  ratio  between  degrees,  which  is 
as  5:9.  This  dotted  line  is  to  be  used  in  converting 
rise  in  temperature  from  one  scale  into  the  other. 

173.   HEATING  EFFECT 

An  electric  current  flowing  through  a  winding  gen- 
erates heat  therein  proportional  to  the  watts  lost  in  the 
winding.  If  the  winding  consists  of  good  heat-con- 
ducting material,  and  ample  surface  is  provided  for 
the  radiation  of  the  heat,  much  more  energy  may  be 
applied  than  if  the  winding  be  poorly  designed. 

Much  regarding  the  heat-resisting  qualities  and  heat- 
conducting  properties  of  insulating  materials  was  men- 
tioned in  Chapter  XVII.  It  is  obvious  that  heat  may 
be  conducted  through  a  thin  winding  much  faster  than 
through  a  thick  one. 

Experience  has  shown  that  a  coil  of  ordinary  dimen- 
sions may  remain  in  circuit  continuously  when  the  ap- 


HEATING  OF  ELECTROMAGNETIC   WINDINGS      299 

plied  electrical  power  does  not  exceed  0.50  watt  per 
square  inch  of  superficial  radiating  surface. 

Coils  mounted  on  large  iron  cores  which  in  turn  are 
attached  to  the  frames  of  machines  have  an  advantage 
in  the  fact  that  the  core  conducts  the  heat  away  where 
it  can  be  radiated  rapidly. 

174.   TEMPERATURE  COEFFICIENT 

Most  of  this  article,  as  well  as  the  data  from  which 
Fig.  213  was  made,  is  taken  from  the  Standardization 
Rules  of  the  American  Institute  of  Electrical  Engineers. 

The  fundamental  relation  between  the  increase  of  re- 
sistance in  copper  and  the  rise  of  temperature  may  be 
taken  as 

Et  =  E0(l  +  0.  0042  0,  (328) 

where  R0  is  the  resistance  at  t°  C.  of  the  copper  con- 
ductor at  0°  C.,  and  Rt  is  the  corresponding  resistance. 
This  is  equivalent  to  taking  a  temperature  coefficient 
of  0.42  per  cent  per  degree  C.  temperature  rise  above 
0°  C.  For  initial  temperatures  other  than  0°  C.,  a 
similar  formula  may  be  used,  substituting  the  coeffi- 
cients in  Fig.  213  corresponding  to  the  actual  tempera- 
ture. The  formula  thus  becomes  at  25°  C., 

0-3801 


where  Rt  is  the  initial  resistance  at  25°  C.,  Ri+r  the  final 
resistance,  and  r  the  temperature  rise  above  25°  C. 

In  order  to  find  the  temperature  rise  in  degrees  C. 
from  the  initial  resistance  Rt  at  the  initial  temperature 
*°  C.,  and  the  final  resistance  Ri+r,  use  the  formula 

r  =  (238.1  +  0-1  (330) 


300 


SOLENOIDS 


00 


35 
C 


5 


HEATING  OF   ELECTROMAGNETIC   WINDINGS      301 


V) 

^  ^ 

il 


302  SOLENOIDS 

The  amount  of  applied  energy  depends  upon  the  place 
where  the  coil  is  to  be  used. 

The  resistance  of  a  winding  at  the  limiting  tempera- 
ture will,  therefore,  be 

w 
H(+r  =  -~,  (331) 

A3r 

wherein  W=  total  energy  in  coil,  and  Sr  is  the  radiat- 
ing surface. 

175.    HEAT  TESTS 

Experimental  data  for  any  particular  coil  may  be  ob- 
tained by  placing  thermal  coils,  which  consist  of  a  few 
turns  of  small  wire,  at  different  points  in  the  winding. 
The  rise  in  resistance  of  these  coils  will  determine  the 
rise  in  temperature  of  the  winding,  observations  being 
taken  from  time  to  time,  from  which  data  a  curve  may 
be  plotted.  Such  a  curve  is  shown  in  Fig.  214,  which 
is  the  result  of  a  test  of  the  small  iron-clad  solenoid  of 
dimensions  Z=4.6  cm.,  ra  =  1.3  cm.  (See  p.  108.) 
The  winding  should  be  designed  for  a  rise  in  tempera- 
ture considerably  lower  than  that  shown  in  the  illus- 
tration, when  silk  or  cotton  insulation  is  used. 

176.    ACTIVITY  AND  HEATING 

What  was  said  in  Art.  132  applies  particularly  to 
coils  which  are  to  be  left  in  circuit  indefinitely. 

The  greater  the  activity  of  the  winding,  the  less  will 
be  the  energy  required,  and,  consequently,  the  less  will 
be  the  heating,  for  an  electromagnet  of  given  dimensions. 

Electromagnets  for  operating  trolley  signals  some- 
times have  a  resistance  of  several  thousand  ohms,  de- 
pending upon  the  time  they  are  to  remain  in  circuit. 


HEATING  OF  ELECTROMAGNETIC   WINDINGS      303 

As  a  matter  of  fact,  it  is  best  to  make  magnets  of  this 
character  "  Fool-proof,"  by  so  designing  the  winding 
that  the  current  may  be  left  on  continuously  without 
overheating  the  coil. 

The  resistance  of  a  winding  which  is  to  be  left  in  cir- 
cuit continuously  will  vary  with  the  radiating  surface. 

For  a  very  large  magnet  the  resistance  may  be  only 
a  few  hundred  ohms,  while  for  a  small  one  it  may  be 
several  thousand  ohms.  The  figures  given  apply,  of 
course,  to  high-voltage  apparatus. 

A  magnet  which  is  to  be  left  in  circuit  indefinitely 
must,  necessarily,  be  larger  than  one  which  is  to  exert 
the  same  pull  through  the  same  distance,  but  to  only  re- 
main in  circuit  for  a  short  time  and  then  remain  idle. 

A  large  electromagnet  lias  a  greater  winding  volume 
than  a  small  one  ;  hence,  its  resistance  may  be  much 
greater  without  greatly  increasing  the  average  perimeter 
and,  therefore,  without  greatly  reducing  the  ampere- 
turns. 

By  slightly  increasing  the  thickness  of  the  winding 
the  resistance  will  be  correspondingly  increased,  and 
the  heating  reduced  without  greatly  reducing  the  am- 
pere-turns for  the  same  size  of  wire. 

A  winding  completely  enclosed  in  an  iron  shell  may, 
if  the  space  between  the  winding  and  shell  be  prop- 
erly filled  with  a  good  heat-conducting  insulating  com- 
pound, have  approximately  50  per  cent  more  energy 
applied  to  it  per  unit  surface  area  than  if  the  coil  were 
exposed  to  the  open  air.  This  will,  of  course,  depend 
upon  the  radiating  surface  of  the  shell  through  which 
the  heat  is  conducted  from  the  winding. 


CHAPTER   XXI 
TABLES  AND  CHARTS 

THE  following  tables  and  charts  have  been  placed  in 
a  separate  chapter  in  order  to  make  them  easily  acces- 
sible for  reference.  The  factors  given  for  insulated 
wires  are  those  which  have  been  found  to  give  the  best 
results  in  practice.  The  weights  of  insulated  wire  are, 
however,  for  perfectly  dry  insulation,  and  in  practice 
they  may  appear  too  low,  owing  to  the  hygroscopic 
properties  of  the  insulating  material. 

The  factors  are  expressed  in  English  units.     Thus, 

d  =  diameter  of  bare  wire  in  inch. 

d1  =  diameter  of  insulated  wire  in  inch. 

pi  =  ohms  per  inch. 

pw  =  ohms  per  pound  for  bare  wires. 

pv  =  ohms  per  cubic  inch  for  insulated  wires. 
Wv  =  pounds  per  cubic  inch  for  insulated  wires. 
Na  =  turns  per  square  inch. 

The  temperature  for  which  these  tables  and  charts 
have  been  calculated  is  20°  C.  or  68°  F. 


304 


TABLES  AND   CHARTS 


305 


STANDARD  COPPER  WIRE  TABLE* 

Giving  weights,  lengths,  and  resistances  of  wires  at  20°  C.  or  68°  F.,  of 
Matthiessen's  Standard  Conductivity,  for  A.  W.  G.  (Brown  &  Sharpe). 


A.W.G. 

DIAME- 
TER 

AREA 

WEIGHT 

LENGTH 

RESISTANCE 

B.&S. 

Inches 

Circular 
Mils 

Lbs. 
per  Ft. 

Lbs. 
per  Ohm 

Feet 
perLb. 

Feet 
per  Ohm 

Ohms 
per  Lb. 

Ohms 
per  Ft. 

oooo 

460 

211,600 

6405 

13,090 

1.561 

20,440 

.00007639 

.00004893 

000 

4096 

167,800 

5080 

8,232 

1.969 

16,210 

.0001215 

.00006170 

oo 

3648 

133,100 

4028 

5,i77 

2.482 

12,850 

.0001931 

.00007780 

0 

3249 

105,500 

3i95 

3,256 

3-130 

10,190 

.0003071 

.00009811 

I 

2893 

83,690 

2533 

2,048 

3-947 

8,083 

.0004883 

.0001237 

2 

2576 

66,370 

2009 

1,288 

4-977 

6,410 

.0007765 

.0001560 

3 

2294 

52,630 

1593 

810.0 

6.276 

5,084 

.001235 

.0001967 

4 

2043 

41,740 

1264 

509-4 

7.914 

4,031 

.001963 

.0002480 

5 

1819 

33,ioo 

1002 

320.4 

9.980 

3,i97 

.003122 

.0003128 

6 

1620 

26,250 

07946 

201.5 

12.58 

2,535 

.004963 

.0003944 

7 

1443 

20,820 

.06302 

126.7 

15-87 

2,0  1  1 

.007892 

.0004973 

8 

.1285 

16,510 

04998 

79.69 

20.01 

1,595 

•01255 

.0006271 

9 

.1144 

13,090 

•03963 

50.12 

25-23 

1,265 

•01995 

.0007908 

10 

.1019 

10,380 

•03143 

31-52 

31.82 

1,003 

•03173 

.0009972 

ii 

.09074 

8,234 

•02493 

19.82 

40.12 

795-3 

•05045 

.001257 

12 

.08081 

6,530 

.01977 

12.47 

50.59 

630.7 

.08022 

.001586 

13 

.07196 

5-178 

.01568 

7.840 

63-79 

500.1 

.1276 

.001999 

14 

.06408 

4,107 

.01243 

4-931 

80.44 

396.6 

.2028 

.002521 

15 

.05707 

3,257 

.009858 

3.101 

101.4 

314.5 

•3225 

.003179 

16 

.05082 

2,583 

.007818 

1.950 

127.9 

249.4 

.5128 

.004009 

17 

•04526 

2,048 

.006200 

1.226 

161.3 

197-8 

•8153 

.005055 

18 

.04030 

1,624 

.004917 

7713 

203.4 

156.9 

1.296 

.006374 

19 

•03589 

1,288 

.003899 

4851 

256.5 

124.4 

2.061 

.008038 

20 

.03196 

1,022 

.003092 

•3051 

323-4 

98.66 

3.278 

.01014 

21 

.02846 

SlO.I 

.002452 

.1919 

407.8 

78.24 

5.212 

.01278 

22 

•02535 

642.4 

.001945 

.1207 

514-2 

62.05 

8.287 

.01612 

23 

.02257 

509.5 

.001542 

.07589 

648.4 

49.21 

13-18 

.02032 

24 

.02010 

404.0 

.001223 

•04773 

817.6 

39.02 

20.95 

•02563 

25 

.01790 

320.4 

.0009699 

.03002 

1,031 

30-95 

33-32 

.03231 

26 

.01594 

254-1 

.0007692 

.01888 

1,300 

24-54 

52-97 

.04075 

27 

.0142 

201.5 

.OOo6lOO 

.01187 

1,639 

19.46 

84.23 

.05138 

28 

.01264 

159.8 

•0004837 

.007466 

2,067 

15-43 

133-9 

.06479 

29 

.01126 

126.7 

.0003836 

.004696 

2,607 

12.24 

213.0 

.08170 

3° 

.01003 

IOO-5 

.0003042 

.002953 

3,287 

9.707 

338.6 

.1030 

3i 

.008928 

79.70 

.0002413 

.001857 

4,145 

7.698 

538.4 

.1299 

32 

.007950 

63.21 

.0001913 

.001168 

5,227 

6.105 

856.2 

.1638 

33 

.007080 

50.13 

.0001517 

.0007346 

6,591 

4.841 

1,361 

.2066 

34 

.006305 

39-75 

.OOOI2O3 

.0004620 

8,311 

3-839 

2,165 

.2605 

35 

.005615 

31-52 

.00009543 

.0002905 

10,480 

3-045 

3,44i 

•3284 

36 

.0050 

25-0 

.00007568 

.0001827 

13,210 

2.414 

5,473 

.4142 

37 

•004453 

19.83 

.OOOO6OOI 

.0001149 

16,660 

I.9I5 

8,702 

.5222 

38 

.003965 

15-72 

.00004759 

.00007210 

21,010 

I.5I9 

13,870 

•6585 

39 

•003531 

12.47 

.00003774 

.00004545 

26,500 

1.204 

22,000 

.8304 

40 

.003145 

9.888 

.00002993 

.00002858 

33,410 

•9550 

34,980 

1.047 

*  Supplement  to  Transactions  of  American  Institute  of  Electrical  Engineers,  October,  1893. 


306 


SOLENOIDS 


METRIC   WIRE  TABLE 

Calculated  by  the  author,  using  the  same  constants  and  temperature  co- 
efficients as  in  the  Standard  Copper  Wire  Table,  p.  305. 


A.W.  G. 

DIAME- 
TER 

AREA 

WEIGHT 

LENGTH 

RESISTANCE 

B.  &S. 

Mm. 

Sq.  Mm. 

Kg. 
perM. 

Kg. 
per  Ohm 

M. 
per  Kg. 

M. 

per  Ohm 

Ohms 
per  Kg. 

Ohms 
perM. 

0000 

11.7 

107.2 

•953 

5940 

1.05 

62,300 

.000168 

.0000161 

ooo 

10.4 

85.0 

•756 

3730 

1.32 

49,4oo 

.000268 

.0000202 

00 

9.27 

67.4 

•599 

2350 

1.67 

30,200 

.000426 

.0000255 

0 

8.25 

53-5 

•475 

1480 

2.10 

31,100 

.000677 

.0000322 

I 

7-35 

42.4 

•377 

929 

2.65 

24,600 

.00108 

.0000406 

2 

6-54 

33-6 

•299 

584 

3-35 

19,500 

.00171 

.0000512 

3 

5.83 

26.7 

•237 

367 

4.22 

15,500 

.00272 

.0000645 

4 

5-19 

21.2 

.188 

231 

5-32 

12,300 

•00433 

.0000814 

5 

4.62 

16.8 

.149 

i45 

6.71 

9,750 

.00688 

.000103 

6 

4.11 

13-3 

.118 

91.4 

8.46 

7,730 

.0109 

.000129 

7 

3.67 

10.6 

.0938 

57-5 

10.7 

6,130 

.0174 

.000163 

8 

3-26 

8-37 

.0744 

36.2 

13-5 

4,860 

.0277 

.000206 

9 

2.91 

6.63 

.0590 

22.7 

17.0 

3,86o 

.0440 

.000259 

10 

2-59 

5.26 

.0468 

14-3 

21.4 

3,060 

.0699 

.000327 

ii 

2.31 

4.17 

•0371 

8-99 

27.0 

2,420 

.in 

.000413 

12 

2.05 

3-31 

.0294 

5-66 

34-o 

1,920 

.177 

.000520 

13 

1.83 

2.62 

.0234 

3-56 

42.9 

i,530 

.281 

.000656 

14 

1.63 

2.08 

.0185 

2.24 

54-1 

1,210 

•447 

.000827 

IS 

1-45 

1.65 

.0147 

1.41 

68.2 

959 

.711 

.00104 

16 

1.29 

J-31 

.0116 

.885 

86.0 

760 

1-13 

.00132 

17 

i-iS 

1.04 

.00922 

•556 

1  08 

603 

1.80 

.00166 

18 

i.  02 

.823 

.00732 

•350 

136 

478 

2.86 

.00209 

19 

.912 

.653 

.00580 

.220 

172 

379 

4-54 

.00264 

20 

.812 

.518 

.00460 

•  138 

217 

301 

7-23 

•00333 

21 

•  723 

.410 

.00365 

.0871 

274 

239 

n-5 

.00419 

22 

.644 

.326 

.00289 

.0548 

346 

189 

18.3 

.00529 

23 

•573 

.258 

.00229 

•0344 

436 

150 

29.1 

.00667 

24 

•5ii 

.205 

.00182 

.0217 

550 

119 

46.2 

.00841 

25 

•455 

.162 

.00144 

.0136 

693 

94-3 

73-4 

.0106 

26 

.40  5 

.129 

.00114 

.00856 

874 

74-8 

117 

.0134 

27 

.361 

.102 

.000908 

.00538 

1,100 

59-3 

1  86 

.0169 

28 

.321 

.O8l 

.000720 

•00339 

1,390 

47-0 

295 

.0213 

29 

.286 

.0642 

.000571 

.00213 

1.750 

37-3 

470 

.0268 

30 

•255 

.0510 

.000453 

.00134 

2,210 

29.6 

747 

•0338 

31 

.227 

.0404 

.000359 

.000842 

2,790 

23-5 

1,190 

.0426 

32 

.202 

.0320 

.000285 

.000530 

3,5io 

18.6 

1,890 

•0537 

33 

.ISO 

.0254 

.000226 

.000333 

4,430 

14.8 

3,000 

.0678 

34 

.l6o 

.O2OI 

.000179 

.000210 

5,590 

11.7 

4,770 

•0855 

35 

•143 

.Ol6o 

.000142 

.000132 

7,040 

9.28 

7,590 

.108 

36 

.127 

.0127 

.000113 

.0000829 

8,880 

7.36 

12,100 

.136 

37 

•I:[3 

.OIOI 

.0000893 

.0000521 

11,200 

5-84 

I9,2OO 

.171 

38 

.101 

.00797 

.0000708 

.0000327 

14,100 

4-63 

30,600 

.216 

39 

.0897 

.00632 

.0000562 

.OOOO2O6 

17,800 

3-67 

48,500 

•  273 

40 

.0799 

.00501 

.0000445 

.0000130 

22,500 

2.91 

77,100 

•344 

TABLES   AND  CHARTS 


307 


o  H  «  m+wo  ^oo  0,0  M 


11 

|CO 


in  j  o 


10 

1 5" 


t-    2~ 


ooooovom-*- 


1± 

_!«_ 

I  o 


o      oo  coo 


COl    HI    NO    OO    COOOOO 
M    |     rj-  CO  N    (N    HI    HI    HI 


MO^oo^oroo 

^OlO    <N    HI    HI    HI 


<»    |    gig1' 


2      bocoooooin-^-cf 

"I       <N     M     M     M 


(^   I   N*O  0*0  co  c?co  o1 10  *5-  cov 

~iO~CMH~tx  •$•  O    CO  N    IT)  <N    HI    i 

HI  <No  oo  cooooo  in  Tf 


I    fH 

I  « 


Tj-O    COW    -t»O  ON  M    tx-fO    CON    LOO)    HI    (NO    OO 
<N    u->  COO    <NM<NOOOrOOoOOlO^f-CO«<NHI 

roooooto-^-rooi  <N  M  M  M 


I    OrhOcOHiT^uoON 

>O  O    -1-  O    CO~HI    -^-  u-,  o  M    t^-^-O    CON   inN   HI 

o  t^x  (N  in  coo  N  HI  do  oo  cooooo  in  ^± 

MOCOOOOOm^-CONNMHIHi 


i  O  co  O  oo  vo  *mi- 


OOH 


O\0  M 


srss^sa 


308 


SOLENOIDS 


BARE   COPPER  WIRE 


B.&S. 
No. 

d 

d3 

Pi 

Pw 

o 

.3249 

.10550 

.000008176 

.0003071 

i 

.2893 

.08369 

.OOOOI03I 

.0004883 

2 

.2576 

.06637 

.OOOOI300 

.0007765 

3 

.2294 

.05263 

.OOOOI639 

.001235 

4 

.2043 

.04174 

.OOOO2O67 

.001963 

5 

.1819 

.03310 

.OOOO2607 

.003122 

6 

.1620 

.02625 

.00003287 

.004963 

7 

•1443 

.O2O82 

.00004144 

.007892 

8 

.1285 

.01651 

.00005226 

.01255 

9 

.1144 

.01309 

.00006590 

.01995 

10 

.1019 

.01038 

.000083IO 

.03173 

ii 

.09074 

.008234 

.0001048 

.05045 

12 

.08081 

.006530 

.0001322 

.08022 

J3 

.07196 

.005178 

.OOOI667 

.1276 

14 

.06408 

.004107 

.O002IOI 

.2028 

J5 

.05707 

.003257 

.0002649 

.3225 

16 

.05082 

.002583 

.0003341 

.5128 

17 

.04526 

.002O48 

.0004213 

•8153 

18 

.04030 

.001624 

.0005312 

1.296 

19 

•03589 

.001288 

.0006698 

2.o6l 

20 

.03196 

.001022 

.000845 

3.278 

21 

.02846 

.0008IOI 

.001065 

5-212 

22 

•02535 

.0006424 

.001343 

8.287 

23 

.02257 

.0005095 

.001693 

I3.I8 

24 

.02010 

.0004040 

.002136 

20.95 

25 

.01790 

.0003204 

.002693 

33-32 

26 

.01594 

.0002541 

.003396 

52.97 

27 

.01420 

.0002015 

.004282 

84.23 

28 

.01264 

.0001598 

•005399 

I33-9 

29 

.OII26 

.0001267 

.006808 

213.0 

30 

.01003 

.0001005 

.008583 

338.6 

31 

.008928 

.OOOO7970 

.01083 

538.4 

32 

.007950 

.00006321 

.01365 

856.2 

33 

.007080 

.00005013 

.01722 

1,361 

34 

.006305 

.00003975 

.02171 

2,165 

35 

.005615 

.00003152 

.02737 

3,441 

36 

.005OOO 

.00002500 

•03452 

5,473 

37 

•004453 

.00001983 

.04352 

8,702 

38 

.003965 

.00001572 

.05488 

13,870 

39 

.003531 

.00001247 

.06920 

22,000 

40 

.003145 

.00009888 

.08725 

34,980 

TABLES  AND  CHARTS 


309 


T$ 


Otr 

ee 

8£ 
.*£ 
9£ 


~/L 


€£ 
^f 
/f 


4Z 
9? 

^r 
tr 
o^ 

€/ 

^/ 

P/ 

s-/ 
>•/ 
£/ 

r/ 
// 


ex    ^    o 
«x    M    ex 

0^000 


a  ^ 
5 


W>     ^     5     cy 

$6^5 


"NO 
o    o    o 


<7/V/70</ 


310 


SOLENOIDS 


VALUES  OF  d\  FOR  DIFFERENT  THICKNESSES  OF  INSULATION 


No.  B.  &  S. 

lo-MiL 

5-MiL 

10 

.1119 

.1069 

ii 

.1007 

•0957 

12 

.0908 

.0858 

13 

.0820 

.0770 

14 

.0741 

.0691 

15 

.0671 

.0621 

16 

.0608 

.0558 

17 

•0553 

.0503 

18 

•0503 

•0453 

19 

•0459 

.0409 

8-MiL 

4-MiL 

2-MlL 

20 

.0400 

.0360 

.0340 

21 

•0365 

•0325 

.0305 

22 

•0334 

.0294 

.0274 

23 

.0306 

.0266 

.0246 

24 

.0281 

.0241 

.0221 

25 

.0259 

.0219 

.0199 

26 

.0239 

.0200 

.0179 

27 

.0222 

.0182 

.Ol62 

28 

.0206 

.0166 

.0146 

29 

.0193 

•0153 

•0133 

30 

.Ol8o 

.0140 

'  .0120 

31 

.0170 

.0130 

.0109 

32 

.Ol6o 

.0120 

.00995 

33 

.0151 

.OIII 

.00908 

34 

.0143 

.0103 

.00830 

35 

.0136 

.0096 

.00761 

36 

.0130 

.009O 

.00700 

3-MiL 

1.5-MiL 

37 

.00745 

.0060 

38 

.00697 

•0055 

39 

.00653 

.00503 

40 

.00615 

.00465 

TABLES   AND   CHARTS 


311 


TABLE  SHOWING  VALUES  OF  Na  (TURNS  PER  SQUARE  INCH),  FOR 
DIFFERENT  THICKNESSES  OF  INSULATION 


No.  B.  &  S. 

10-MlL 

S-MiL 

10 

80 

87 

II 

98 

109 

12 

121 

135 

*3 

149 

168 

14 

182 

210 

15 

222 

260 

16 

27O 

321 

J7 

328 

396 

18 

396 

487 

19 

476 

599 

8-MiL 

4-MiL 

2-MlL 

20 

627 

775 

869 

21 

752 

95o 

1,075 

22 

900 

1,160 

J,335 

23 

1,070 

1,420 

1,655 

24 

1,270 

i,725 

2,050 

25 

1,490 

2,090 

2,520 

26 

1,740 

2,520 

3,090 

27 

2,025 

3,010 

3,810 

28 

2,350 

3,610 

4,680 

29 

2,700 

4,3°° 

5,690 

3° 

3,080 

5,080 

6,900 

31 

3,49° 

6,000 

8,370 

32 

3,930 

7,000 

10,100 

33 

4,400 

8,140 

12,100 

34 

4,880 

9,45o 

14,500 

35 

5,400 

10,800 

17,250 

36 

5,920 

12,350 

20,400 

3-MiL 

i.S-MiL 

37 

l8,000 

28,200 

38 

2O,6oo 

33,400 

39 

23,450 

39,500 

40 

26,450 

46,250 

312 


SOLENOIDS 


BLACK  ENAMELED  WIRE* 

(Approximate  Values) 


No.  B.  &  S. 

FEET  PER  POUND 

TURNS  PER  SQUARE  INCH 

(Na) 

24 

810 

2,162 

25 

1,019 

2,75° 

26 

1,286 

3,460 

27 

1,620 

4,270 

28 

2,042 

5,406 

29 

2,570 

6,608 

30 

3,240 

8,264 

31 

4,082 

10,832 

32 

5,132 

13,428 

33 

6,445 

16,832 

34 

8,093 

21,002 

35 

10,197 

26,014 

36 

12,813 

31,822 

37 

16,110 

43,402 

38 

20,274 

54,082 

39 

25,519 

69,390 

40 

32,107 

86,504 

*  American  Electric  Fuse  Co. 


TABLES  AND  CHARTS 


313 


DELTABESTON  WIRE  TABLE  * 


WIRE  SIZE 
B.  &S. 

DIAMETER 
DRAWN  MILS 

OUTSIDE 
DIAMETER 
DELTABESTON 

CIRCULAR 
MILS 

RESISTANCE  IN 
OHMS  PER 
1000  FEET 

M 

g<i 

*Q 

s§ 
££ 

FEET  PER 
POUND 
DELTABESTON 

POUNDS  PER 
1000  FEET 
DELTABESTON 

oo 

.3648 

133,079 

.0789 

2.485 

0 

•3250 

•343 

105,625 

.0994 

3-131 

I 

.2893 

•307 

83,694 

•!255 

3-952 

3-88 

257-73 

2 

.2576 

.276 

66,358 

.1583 

4.984 

4.90 

204.08 

3 

.2294 

.247 

52,624 

.1996 

6.285 

6.15 

162.60 

4 

.2043 

.220 

41,738 

.2516 

7.924 

7.70 

129.87 

5 

.1819 

.198 

33-088 

•3J74 

9.996 

9.70 

103.09 

6 

.1620 

.178 

26,244 

.4002 

12.60 

12.2 

81.97 

7 

.1443 

.160 

20,822 

•  5°44 

15.88 

15.4 

64.93 

8 

.1285 

.142 

16,512 

.6361 

20.03 

19-5 

51.28 

9 

.1144 

.128 

13,087 

.8026 

25.27 

24-5 

40.82 

10 

.1019 

.116 

10,384 

I.OII 

31-85 

30.8 

32.47 

ii 

.0907 

.103 

8,226 

1.277 

40.21 

37-9 

26.38 

12 

.0808 

•093 

6,527 

1.609 

50.66 

46.7 

21.41 

13 

.0720 

.082 

5,184 

2.026 

63.80 

58.4 

17.12 

14 

.0641 

.074 

4,109 

2-556 

80.50 

73-2 

13.66 

15 

•0571 

.067 

3,260 

3.221 

101.4 

91.7 

10.90 

16 

.0508 

.061 

2,581 

4.070 

128.2 

114.4 

8.74 

17 

•0453 

•055 

2,052 

5.118 

161.2 

145 

6.90 

18 

.0403 

.050 

1,624 

6.466 

203.7 

183 

5.46 

19 

•°359 

.046 

1,289 

8.151 

256.6 

231 

4-33 

20 

.0320 

.042 

1,024 

10.26 

323-0 

*  D.  &  W.  Fuse  Co. 


314 


SOLENOIDS 


.100 
.095 

tt         -090 
|        .085 
u.  w    -080 

°  s  - 

vr 

*U-f* 

\\ 

1 

\ 

V- 

NO. 

.«_L 

_*. 

\\ 

1 

^v 

NO 

A, 

_«. 

S 

E  -  *OT0' 
1  ~  'o65 

0          .050 

s 

x. 

^ 

IT 

^ 

to" 

!?y 

^ 

jr 

NOT 

« 

.055 
.060, 

•  — 

NO. 

ttt 

'OHMS  PER  CUBIC'INCH' 

!M? 

FIG.  216.  —  f>»  Values.    Nos.  10  to  16,  B.  &  S. 


•Sst- 

M 

A 

W 

• 

8 

=ns 

ii 

-1 

v^\ 

£     £ 

\\ 

\\ 

>  •*  .041 

4f 

V 

\N 

^ 

H 

^ 

s\ 

\s, 

^ 

5  °    03S 

\ 

*v 

\\ 

V 

(N 

N 

1-  Z    017 

\ 

S 

\ 

\ 

ul   ^'°37 
^         «036 

; 

N 

i^ 

X 

X! 

N 

Ob 

.is 

rE 

r< 

=l 

<         .035 

u 

| 

2 

k- 

^ 

^ 

| 

< 

5 

At 

it 

.03? 

. 

^2 

^ 

^ 

<5 

rt3 

5 

^ 

"t 

--. 

'7 

a 

-^. 

^* 

^* 

^^ 

-  —  , 

*--- 

^-r 

~-« 

.079 

._ 

- 

4- 

^, 

^ 

c~ 

— 

"~~i 

^ 

>- 

^ 

r~ 

=5 

•S 

S,     g.     S     8     S     S     ft     5     3.     8     S     S     3     8     !?     S.     S.     S 

'OHMS  PER  CUBIC  INCH 

\     8.     g      S     2     S     8 

FIG.  217.  —  pv  Values.    Nos.  16  to  21,  B.  &  S. 


TABLES  AND  CHARTS 


315 


1=         >0 

OHMS  PER  CUBIC  INCH 


FIG.  218.  -  pv  Values.    Nos.  21  to  26,  B.  &  S. 


>0090u_± 


OHMS  PER  CUBIC  INCH 

FIG.  219.  —  pv  Values.    Nos.  26  to  31,  B.  &  S. 


316 


SOLENOIDS 


.ooss   -• 

m& 

\ 

[\V\V\ 

\  \K 

^ 

^ 

.0060     - 

m 

.0076     - 
.0076     -  - 

T\\\ 

" 

i^- 

^ 

V 

K 

e 

.0012    - 

\'  \ 

\ 

\ 

f 

.C070     -- 

=    j 

3S 

S 

k 

t 

x1 

f 

P 

V 

k 

' 

j 

'ooM 

\ 

\ 

\ 

•x. 

k 

rK 

» 

.0062.    - 

\ 

^~ 

^ 

\ 

s 

s 

"^     s^ 

•*•  ^ 

*    «:   KJ 

\ 

^ 

^, 

s; 

^x, 

•^  ^ 

-- 

-ff 

B_ 

=.< 

s 

X, 

* 

--, 

<K53 

v 

^^  ^ 

—  1— 

f- 

E 

,0040  Li- 

-SI!IIllllIl|SIll|lfS||g|2?§§§i|S|2Sf| 
OHMS  PER  CUBIC  INCH. 

Fia.  220.— ^Values.    Nos.  31  to  36,  B  &  S. 


OHMS  PER  CUBIC  INCH 

Fia.  221.  —  pv  Values.    Nos.  36  to  40,  B.  &  S. 


TABLES  AND  CHARTS 


317 


RESISTANCE   WIRES* 

(Ohms  per  1000  feet) 


No.  B.  &  S. 

FERRO-NICKEL 

S.  B. 

MANGANIN 

I 

2.0 

2 

2-5 

3 

3-2 

4 

4.1 

5 

5.1 

6 

6.5 

7 

8.2 

8 

10.4 

9 

13.1 

10 

16.3 

32 

ii 

20.5 

40 

12 

25.9 

51 

13 

32.7 

64 

14 

41.5 

82 

15 

52.3 

103 

76 

16 

65-4 

130 

94 

17 

85 

168 

122 

18 

1  06 

2IO 

153 

19 

131 

260 

I89 

20 

1  66 

328 

244 

21 

209 

415 

3OI 

22 

266 

525 

382 

23 

333 

660 

480 

24 

425 

831 

606 

25 

53  1 

1,050 

765 

26 

672 

1,328 

968 

27 

850 

1,667 

1,212 

28 

1,070 

2,112 

1,540 

29 

i,33o 

2,625 

1,910 

30 

1,700 

3,360 

2,448 

31 

2,120 

4,250 

3,090 

32 

2,660 

5,250 

3,825 

33 

3,400 

6,660 

4,857 

34 

4,250 

8,400 

6,166 

35 
36 

5,400 
6,800 

IO,7OO 
13,440 

7,796 
9,792 

37 

16,640 

12,363 

38 

2I,OOO 

15,692 

39 

27,540 

19,742 

40 

37,300 

24,980 

*  Driver-Harris  Wire  Co. 


318 


SOLENOIDS 


PROPERTIES   OF    "NICHROME"    RESISTANCE    WIRE* 

Resistance  per  mil-foot  at  75°  Fahr.  —  575  ohms. 
Temperature  coefficient  —  .00024  Per  degree  Fahr. 
Specific  gravity  —  8.15. 


No. 
B.  &S. 

DIAMETER 
IN  INCHES 

AREA  IN  CIR- 
CULAR MILS 
C.  M.-D2 

RESISTANCE 

PER    1000    FT. 

AT  75°  F. 

WEIGHTS 

PER  1000  FT. 

BARE 

OHMS 
PER  POUND 

I 
2 

3 
4 

5 

.289 

.258 
.229 
.204 
.182 

83,521 
66,564 

52,441 
41,616 

33»££4 

6-9 

8.5 

II.O 

13.8 

17-3 

231 
184 

J45 
H5 
92 

.029 
.046 
•    .076 

.12 

.188 

6 

7 
8 

9 

10 

.162 
.144 
.128 
.114 
.102 

26,244 
20,736 
16,384 
12,996 
10,404 

21.9 

27.7 

35-i 
44-2 

55-2 

73 
57 
45 
36 
29 

.300 
.485 
.78 
1.22 
1.90 

ii 

12 
13 

14 

15 

.091 
.O8l 
.072 
.064 
•057 

8,281 
6,561 
5,184 
4,096 
3,249 

69-5 

87.7 

no 

140 
177 

23- 
18. 

14-3 
"•3 

9.2 

3.02 

4.85 
7.70 
I2.4 
19-3 

16 

17 
18 

19 

20 

.051 

.045 
.040 
.036 
.032 

2,601 
2,025 
i,  600 
1,296 
1,024 

220 

284 

359 
443 
560 

7-2 
5-6 
4.42 
3-58 
2.83 

30.6 
50-7 
81-3 
124 
198 

21 

22 

23 
24 

25 

.0285 
•0253 
.0226 
.0201 
.0179 

812.3 
640.1 
510.8 
404 
320.4 

710 
900 
1,125 
1,420 
!>795 

2.24 
1.77 
1.41 

1.  12 
.89 

3*7 

508 
800 
1,270 
2,020 

26 

27 
28 
29 
30 

.0159 
.0142 
.0126 
.0113 
.010 

252.8 

201.6 

158.8 
127.7 

100 

2,275 
2,850 
3,620 
4,50° 
5,750 

.70 
.56 

•44 
•35 
.276 

3,25° 
5,100 

8,200 

12,850 
20,800 

31 
32 
33 
34 
35 

.0089 

.008 

.0071 
.0063 
.0056 

79-2 
64 
5°-4 
39-7 
31.4 

7,270 
9,000 
11,400 
14,500 
18,300 

.219 
.177 

•139 
.11 

.087 

33,200 
50,800 
82,000 
132,000 

210,000 

36 

37 
38 
39 
40 

.005 
.0045 

.004 

•0035 
.003 

25 

20.2 

16 

12.2 
9 

23,000 
28,500 
36,000 
47,000 
64,000 

.069 
.056 
•045 
•034 
.025 

333,o°° 
508,000 
800,000 
1,383,000 
2,560,000 

*  Driver-Harris  Wire  Co. 


TABLES  AND  CHARTS 


319 


PROPERTIES  OF  "CLIMAX"   RESISTANCE  WIRE* 

Resistance  per  mil-foot  at  75°  Fahr.  —  525  ohms. 
Temperature  coefficient  —  .0003  per  degree  Fahr. 
Specific  gravity  —  8.137. 


No. 
B.  &S. 

DIAMETER 
IN  INCHES 

AREA  IN  CIR- 
CULAR MILS 
C.  M.-D2 

RESISTANCE 

PER    1000    FT. 

AT  75°  F. 

WEIGHTS 

PER   1000  FT. 

BARE 

OHMS 
PER  POUND 

I 
2 

3 
4 
5 

.289 
.258 
.229 
.204 
.182 

83,521 
66,564 

52,441 
41,616 

33»I24 

6.2 

7-9 

IO.O 
12.6 

15.8 

231 
184 

J45 
"5 
92 

.026 
.041 
.066 
.105 
.165 

6 

7 
8 

9 

10 

.162 
.144 
.128 
.114 

.102 

26,244 
20,736 
16,384 
12,996 

20,404 

20.0 

25-3 
32. 
40.4 

5°-4 

73 
57 
45 
36 
29 

.263 
.427 

-685 
1.  08 
1.65 

ii 

12 
13 
14 
IS 

.091 

.081 
.072 
.064 
.057 

8,281 
6,561 

5,184 
4,096 

3,249 

63-4 
80 

101 

128 
161 

23 

18 

14-3 
n-3 

9-2 

2.70 

4.27 
6.85 
10.9 
16.9 

16 

17 

18 

iQ 

20 

.051 

•045 
.040 
.036 
.032 

2,601 
2,025 
i,  600 
1,296 
1,024 

202 
258 
328 
404 
510 

7-2 

5-6 
4.42 
3.58 
2.83 

27.0 
44-5 
7J-3 
108 

J74 

21 

22 

23 
24 

25 

.0285 
•0253 
.0226 
.O20I 
.0179 

812.3 
640.1 
510.8 
404 
320.4 

646 
820 
I,O27 
1,290 
1,640 

2.24 
1.77 
1.41 

1.  12 
.89 

284 
456 
720 
1,142 
1,810 

26 

27 
28 
29 
30 

.0159 
.0142 
.0126 
.0113 
.010 

252.8 

201.6 

158.8 
127.7 

IOO 

2,080 

2,580 
3,300 

4,100 
5,25° 

'7* 

•56 
•44 

•35 
.276 

2,920 

4,57° 
7,400 
11,560 
18,785 

31 
32 

33 
34 
35 

.0089 
.008 

.0071 

.0063 

.0056 

79-2 
64 
5°-4 
39-7 
3J-4 

6,620 

8,200 

10,410 

13,220 

16,720 

.219 

.177 

•139 
.11 

.087 

29,800 
45,265 
73,214 
118,300 
189,000 

3<> 

H 

39 

40 

.005 

.0045 
.004 

•0035 
.003 

25 

20.2 

16 

12.2 
9 

21,000 
26,000 
33,000 
43,000 
58,000 

.069 
.056 
.045 
•034 
.025 

300,000 
468,000 
733,ooo 
1,264,000 
2,320,000 

*  Driver-Harris  Wire  Co. 


320 


SOLENOIDS 


PROPERTIES  OF   "ADVANCE"   RESISTANCE  WIRE* 

Resistance  per  mil-foot  at  75°  Fahr.  —  294  ohms. 
Temperature  coefficient  —  Nil.     Specific  gravity  —  8.9. 


.w 

&* 

m 

DIAMETER 
IN  INCHES 

AREA  IN  CIR- 
CULAR MILS 
C.  M.-D2 

RESISTANCE 

PER    1000    FT. 

AT  75°  F. 

WEIGHTS 

PER  1000  FT. 

BARE 

OHMS 
PER  POUND 

i 

2 

3 

4 
5 

.289 
•258 
.229 
.204 
.182 

83,521 
66,564 

52,441 
41,616 

33,*24 

3-52 
4.42 
5-6l 
7.07 
8.88 

253 

201 

159 
126 

100 

•01365 
.02174 
.03458 
.05496 
.08742 

6 

8 
9 

10 

.162 
.144 
.128 
.114 

.102 

26,244 
20,736 
16,384 
12,996 

10,404 

II.  21 
14.19 
17.9 
22.6 

28. 

79 
63 

50 
39 

S2 

.13896 
.2209 
•35I4 
.5586 
.888 

ii 

12 
J3 
14 
15 

.091 
.O8l 
.072 
.064 
•057 

8,281 
6,561 
5,184 
4,096 

3,249 

35-5 
44.8 

56.7 
71.7 
90.4 

25 

20 

15-7 
12.4 

9.8 

1.412 
2.246 

3-573 
5.678 
9-03 

16 

*7 

18 

19 

20 

.051 

•045 
.040 
.036 
.032 

2,601 
2,025 
i,  600 
1,296 
1,024 

"3 
I4S 
184 
226 

287 

7.8 

6.2 

4.9 
3-9 
3-1 

14-358 
22.828 
36.288 
57.7o8 
91.784 

21 
22 

23 
24 

25 

.0285 
•0253 
.0226 
.0201 
.0179 

812.3 
640.1 
510.8 
404 
320.4 

362 
460 
575 
725 
919 

2-5 

1.9 
i-5 

1.2 

•97 

145-93 
232.03 
369.04 
586.6 
932.96 

26 
27 
28 
29 
30 

.0159 
.0142 
.0126 
.0113 
.010 

252.8 

2OI.6 

158.8 
127.7 

100 

1,162 

i,455 
1,850 
2,300 
2,940 

•77 
.61 
.48 
.38 
•30 

1,483.16 
2,358 
3,749 
5,964 
9,47° 

31 
32 
33 
34 

35 

.0089 
.008 

.0071 

.0063 

.0056 

79-2 
64 

5°-4 
39-7 
31-4 

3,680 
4,600 
5,830 
7,400 

9,36o 

.24 
.19 
•15 

.12 

•095 

15,075 
23,973 
38,108 
60,620 
96,340 

36 

37 
38 
39 
40 

.005 
.0045 

.004 

•0035 
.003 

25 

20.2 

16 

12.2 
9 

11,760 

i4,55o 
18,375 
24,100 
32,660 

.076 
.060 
.047 
.038 
.028 

153,240 

243,65° 
388,360 
616,000 
1,183,000 

*  Driver-Harris  Wire  Co. 


TABLES  AND   CHARTS 


321 


"MONEL"   WIRE* 

Resistance  per  mil-foot  —  256  ohms. 

Temperature  coefficient  —  .0011.     Specific  gravity  —  8.9. 


CAJ 
1* 

cq 

DIAMETER 
IN  INCHES 

AREA  IN  CIR- 
CULAR MILS 
C.  M.-D* 

RESISTANCE 

PER    1000    FT. 

AT  75°  F. 

WEIGHTS 

PER  1000  FT. 

BARE 

OHMS 
PER  POUND 

0 

I 

2 

3 

4 

5 

.325 
.289 
-258 
.229 
.204 
.182 

105,625 
83,521 
66,564 

52,441 
41,616 

33,124 

2.4 
3-0 
3-8 
4.8 
6.1 
7-7 

317 

253 

2OI 

159 
126 

100 

.0075 
.0118 
.0189 
.0301 
.0484 
.077 

6 

8 
9 

10 

.162 
.144 
.128 
.114 

.102 

26,244 
20,736 
16,384 
12,996 
10,404 

9-8 
12.3 
15-6 
19.7 
24.6 

79 

63 
5° 
39 
32 

.124 
.196 
.312 

•505 
.769 

ii 

12 
13 
14 
15 

.091 
.O8l 
.072 
.064 

-057 

8,281 
6,561 
5,184 
4,096 

3,249 

3°-9 

49-4 
62.6 
78.9 

25 

20 
15-8 
12.4 

9.8 

1-235 
1-955 

5-05 
8.04 

16 

17 
18 

19 

20 

.051 

•045 
.040 
.036 
.032 

2,601 
2,025 
i,  600 
1,296 
1,024 

98.6 

121 
1  60 
I98 

250 

7-8 

6.2 

4-9 
3-9 

3-1 

12.62 

32.69 

50.77 
80.64 

21 

22 

23 
24 

25 

.0285 
•0253 
.O226 
.O2OI 
.0179 

812.3 
640.1 
510.8 
404 
320.4 

315 
4OO 
502 

635 
800 

2-5 

1.9 

1.2 

•97 

126 
210.52 
334-66 
529.16 
824.7 

26 

27 
28 
29 

3° 

.0159 
.OI42 
.0126 
.0113 
.010 

252.8 

201.6 

158.8 
127.7 

100 

991 
1,272 

2,009 
2,566 

•77 
.61 
.48 
•38 
•3° 

1,287 
2,085 

3,365 
5,286 

8,543 

Co  Co  Co  Co  Co 
Cn  4^  Co  to  H 

.0089 
.008 

.0071 
.0063 
.0056 

79-2 
64 
5°-4 
39-7 

3,239 
4,009 

6,463 
8,172 

.24 
.19 

.12 
•095 

13,495 
21,000 

33,940 
53,858 
86,021 

36 
37 
38 
39 
40 

.005 

.0045 

.004 

•0035 
.003 

25 

20.2 

16 

12.2 
9 

IO,26o 
I2,7OO 
16,030 
2I,O30 
28,5IO 

.076 
.060 
.047 
.038 
.028 

135,000 
267,166 
341,063 
553,421 
1,018,214 

*  Driver-Harris  Wire  Co. 


322 


SOLENOIDS 


TABLE  SHOWING  THE   DIFFERENCE   BETWEEN  WIRE 

GAUGES 


No. 

BROWN  & 
SHARPE'S 

LONDON 

BIRMINGHAM 
OR  STUBS 

W.  &  M.  AND 
ROEBLING 

NEW  BRITISH 
STANDARD 

oooo 

000 

oo 

.460 
.40964 
.36480 

•454 
•425 
.380 

•454 
•425 
.380 

•393 

.362 

•33  1 

.400 
•372 

•348 

0 

I 

2 

3 
4 

•32495 
.28930 

.25763 
.22942 

•20431 

•340 
.300 
.284 

•259 

.238 

•340 
•300 
.284 

•259 

•238 

•307 
.283 
•263 
.244 

.225 

.324 
.300 
.276 

.252 
.232 

I 

8 
9 

.18194 
.16202 
.14428 
.12849 
•II443 

.220 
.203 
.ISO 
.165 
.148 

.220 
•203 
.ISO 
•I65 
.148 

.207 
.192 
.177 
.162 

.148 

.212 
.192 
.176 
.160 
.144 

10 

ii 

12 

*3 
14 

.10189 
.09074 
.08081 
.07199 
.06408 

.134 
.120 
.109 

•095 
.083 

•134 
.I2O 
.109 

•095 
.083 

.135 

.120 
.105 
.092 
.080 

.128 
.116 
.104 
.092 

.080 

15 
16 

17 

18 

19 

.05706 
.05082 

•04525 
.04030 

•03589 

.072 
.065 
.058 
.049 

.040 

.072 
.065 
.058 
.049 
.042 

.072 
•063 
•054 

•047 
.041 

.072 
.064 
.056 

.048 
.040 

20 
21 
22 

23 
24 

.03196 
.02846 

•025347 
.022571 

.0201 

•035 
•0315 
.0295 
.027 
.025 

•035 
.032 
.028 
.025 
.022 

•035 
.032 
.028 
.025 
.023 

.036 
.032 
.028 

.024 
.022 

25 
26 
27 
28 
2Q 

.0179 
.01594 
.014195 
.012641 
.011257 

.023 
.0205 
.01875 
.0165 

•OI55 

.O2O 
.018 
.Ol6 
.014 
.013 

.O2O 
.018 
.017 
.Ol6 
.015 

.O2O 
.018 
.0164 
.0148 
.0136 

3° 

31 

32 

33 
34 

.010025 
.008928 
.00795 
.OO7O8 
.0063 

•01375 
.01225 
.01125 
.01025 
.0095 

.OI2 
.OIO 
.009 
.008 

.007 

.OI4 

.0135 
.013 
.Oil 
.OIO 

.0124 
.OIl6 

,OI08 
.010 
.0092 

35 
36 
37 
38 
39 
40 

.00561 
.005 
.00445 
.003965 

•OCtfSai 

.003144 

.009 

.0075 
.0065 
•00575 
.005 
.0045 

.005 
.OO4 

•0095 

.009 

.0085 
.008 
.0075 
.007 

.0084 
.0076 
.0068 
.006 
.0052 
.0048 

TABLES  AND  CHARTS 


323 


PERMEABILITY  TABLE* 


DENSITY  OF 
MAGNETIZATION 

PERMEABILITY,  M 

&' 

Lines  per 
Square  Inch 

6(3 

Lines 
per  Square 
Centimeter 

Annealed 
Wrought 
Iron 

Commercial 
Wrought 
Iron 

Gray 
Cast  Iron 

Ordinary 
Cast  Iron 

20,000 

3,«oo 

2,600 

1,800 

850 

650 

25,000 

3,875 

2,900 

2,000 

800 

700 

30,000 

4,650 

3,000 

2,100 

600 

770 

35,ooo 

5,425 

2,950 

2,150 

400 

800 

40,000 

6,200 

2,900 

2,130 

250 

770 

45,000 

6,975 

2,800 

2,100 

140 

730 

50,000 

7,75o 

2,650 

2,050 

no 

700 

55,000 

8,525 

2,500 

1,980 

90 

600 

60,000 

9,3°° 

2,300 

1,850 

70 

500 

65,000 

10,100 

2,100 

1,700 

5° 

450 

70,000 

10,850 

i,  800 

i,S5° 

35 

350 

75,000 

11,650 

1,500 

1,400 

25 

250 

80,000 

12,400 

1,200 

1,250 

20 

200 

85,000 

13,200 

1,000 

1,100 

15 

15° 

90,000 

14,000 

800 

900 

12 

IOO 

95,000 

14,75° 

530 

680 

IO 

70 

100,000 

i5,5oo 

360 

500 

9 

50 

105,000 

16,300 

260 

360 

110,000 

17,400 

180 

260 

115,000 

17,800 

120 

190 

120,000 

18,600 

80 

I5° 

125,000 

19,400 

50 

120 

130,000 

20,150 

30 

100 

135,000 

20,900 

20 

85 

140,000 

.21,700 

JS 

75 

*  Wiener,  Dynamo  Electric  Machines. 


324 


SOLENOIDS 


TRACTION  TABLE 


a 

LINES  PER  SQUARE 
CENTIMETER 

TRACTION  IN 
KILOGRAMS 
PER  SQUARE 
CENTIMETER 

€&" 

LINES  PER 
SQUARE  INCH 

TRACTION  IN 
POUNDS  PER 
SQUARE  INCH 

1,000 

.4056 

10,000 

1.386 

2,000 

1.622 

15,000 

3-II9 

3,000 

3.650 

20,000 

5-545 

4,000 

6.490 

25,000 

8.664 

5,000 

10.14 

30,000 

12.48 

6,000 

14.60 

35,000 

16.98 

7,000 

19.87 

40,000 

22.18 

8,000 

25.96 

45,000 

28.07 

9,000 

32.85 

50,000 

34-66 

10,000 

40.56 

55,ooo 

41.93 

11,000 

49.08 

60,000 

49.91 

12,000 

58.41 

65,000 

58.57 

13,000 

68.55 

70,000 

67-93 

14,000 

79-50 

75,000 

77-99 

15,000 

91.26 

80,000 

88.72 

16,000 

103.8 

85,000 

IOO.I 

17,000 

117.2 

90,000 

112.3 

18,000 

I3J-4 

95,000 

125.1 

19,000 

146.4 

100,000 

138.6 

*  20,000 

162.2 

105,000 

152.8 

21,000 

178.9 

110,000 

167.8 

22,000 

196.3 

115,000 

183-3 

23,000 

214.6 

120,000 

199.6 

24,000 

233-6 

125,000 

210.6 

25,000 

253.5 

130,000 

234.3 

*The  limit  of  magnetization  for  wrought  iron  is  20,200  lines  per  square  centimeter, 
or  130,000  per  square  inch. 


TABLES  AND   CHARTS 


325 


INSULATING  MATERIALS* 

(Uniform  thickness  and  insulation) 


MATERIAL 

GRADE 

THICKNESS  IN 
MILS 

PUNCTURE  TEST 
IN  VOLTS 

a  x  . 

"  Linen 

A 

6-7 

6,000 

8J^ 

Linen 

AA 

5 

5,000 

S    1 

Linen 

B 

9-10 

9,000 

TS  oil 

Linen 

C 

11-12 

12,000 

^?2 

Canvas 

A 

IO-II 

8,000 

•1*£ 

Canvas 

B 

15-16 

10,000 

F  ^    c 

soJJ 

Black    insulat- 

7, 10,  and  12 

i,  500  per  mil  of 

£  *> 

ing  cloth 

thickness 

*• 

'Paper 

A 

5-6 

5,000 

.s*> 

Paper 

B 

7-8 

8,000 

•g  x 

Paper 

C 

IO-II 

12,000 

<U 

.C5    . 

Red  Rope 

oo  \o   1 

2  ^ 

Paper 

A 

7-8 

7,000 

^^2 

Bond  Paper 

fe  g 

(also  if  X 

•a 

20") 

A 

4-5 

4,000 

Pittsburg  Insulating  Company. 


326 


SOLENOIDS 


o.a  a  i 


0.20 


0.16 


0.10 


0-08 


0.06 


0.04 


0.02 


OJ  0.2  0-3          Ofl          O.5  O.6         O.7         O-8 

t>lAMET£K    IN   INCH 


FIG.  222.  — Weight  per  Unit  Length  of  Plunger. 


TABLES  AND  CHARTS 


327 


X 


3      3      S 


\ 


0        o        o' 


S<7/W70c/ 


328 


SOLENOIDS 


INSIDE  AND  OUTSIDE  DIAMETERS  OF  BRASS  TUBING 

(Inches) 


No.  10  (B.  &  S.)  WALL 

No.  12  (B.  &  S.)  WALL 

Outside 

Inside 

Outside 

Inside 

I* 

1.05 

5 

.465 

if 

LI75 

f 

•59 

if 

1.425 

1 

•715 

I 

.84 

4 

.965 

No.  18  (B.  &  S.)  WALL 

No.  24  (B.  &  S)  WALL 

Outside 

Inside 

Outside 

Inside 

i 

.42 

•545 
.67 

j 

.46 
.585 
•71 

1 

•795 

t 

.835 

I 

.92 

If 

•045 

it 

.17 

i£ 

.42 

if 

.67 

2 

.92 

TABLES  AND  CHARTS 


329 


DECIMAL  EQUIVALENTS 


8ths 

i6ths 

32ds 

64ths 

DECIMAL 
EQUIVA- 
LENT 

8ths 

i6ths 

32ds 

64ths 

DECIMAL 
EQUIVA- 
LENT 

I.  . 

.015625 

O3I  2  ^ 

17 

33  •• 

•5J5625 

.t?3I2:; 

3- 

.046875 
062  5 

Q 

35-- 

.546875 

•  c?62<: 

5- 

.078125 
OQ37  ^ 

IO.  . 

37-- 

•578125 

•59375 

j 

7" 

•109375 
I  2C 

c 

39-  • 

•609375 
.625 

r 

g.. 

.140625 
1^62^ 

21  .  . 

41.  . 

.640625 
.65625 

ii  .  . 

•i7!875 
187=; 

II  .   . 

43-- 

.671875 
.6875 

7 

*3-- 

.203125 
.2187^ 

23  .  . 

45-  • 

.703125 
.71875 

*5" 

•234375 

2C 

47-- 

•734375 
•75 

17.. 

.265625 
28l25 

2C 

49.. 

.765625 
.78125; 

t; 

19.. 

.296875 
•2I2C 

13 

Si-- 

.796875 
.812^ 

II 

21.  . 

.328125 
54-771; 

27.  . 

53- 

.828125 
.84375 

23" 

•359375 
07^ 

55- 

•859375 
871; 

1  3 

25-  • 

.390625 
4.062^ 

2O 

57- 

.890625 
.0062^ 

7 

27.. 

.421875 

4.77  r 

ir 

59- 

.921875 

.Q77C 

I^ 

29.. 

•453J25 
46875; 

31  .  . 

61.. 

•953J25 
.96875 

31- 

•484375 
.500000 

63- 

•984375 

330 


SOLENOIDS 


LOGARITHMS 


No. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

°334 

0374 

ii 

0414 

0453 

0492 

0531 

0569 

0607 

0645 

0682 

0719 

°755 

12 

0792 

0828 

0864 

0899 

C934 

0969 

1004 

1038 

1072 

1106 

13 

1139 

"73 

1206 

1239 

1271 

!3°3 

J335 

1367 

1399 

J43° 

14 

1461 

1492 

1523 

1553 

1584 

1614 

1644 

1673 

1703 

1732 

J5 

1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

17 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

18 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

20 

3010 

3032 

3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

21 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

22 

3424 

3444 

3464 

3483 

3502 

3522 

354i 

356o 

3579 

3598 

23 

36l7 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

24 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

26 

4150 

4166 

4183 

42OO 

4216 

4232 

4249 

4265 

4281 

4298 

27 

43*4 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

29 

4624 

4639 

4654 

4669 

4683 

4698 

47*3 

4728 

4742 

4757 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

32 

5051 

5065 

5079 

5092 

5!°5 

5JI9 

5J32 

5*45 

5*59 

5J72 

33 

5185 

5i98 

5211 

5224 

5237 

5250 

5263 

5276 

5289 

53°2 

34 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

54i6 

5428 

35 

544i 

5453 

5465 

5478 

549° 

5502 

55*4 

5527 

5539 

5551 

36 

5563 

5575 

5587 

5599 

5611 

5623 

5635 

5647 

5658 

5670 

37 

5682 

5694 

5705 

57i7 

5729 

5740 

5752 

5763 

5775 

5786 

38 

5798 

5809 

5821 

5832 

5843 

5855 

5866 

5877 

5888 

5899 

39 

59ii 

5922 

5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

4i 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

42 

6232 

6243 

6253 

6263 

6274 

6284 

6294 

6304 

6314 

6325 

43 

6335 

6345 

6355 

6365 

6375 

6385 

6395 

6405 

6415 

6425 

44 

6435 

6444 

6454 

6464 

6474 

6484 

6493 

6503 

6513 

6522 

45 

6532 

6542 

655i 

6561 

657i 

6580 

6590 

6599 

6609 

6618 

46 

6628 

6637 

6646 

6656 

6665 

6675 

6684 

6693 

6702 

6712 

47 

6721 

6730 

6739 

6749 

6758 

6767 

6776 

6785 

6794 

6803 

48 

6812 

6821 

6830 

6839 

6848 

6857 

6866 

6875 

6884 

6893 

49 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

50 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7°59 

7067 

5i 

7076 

7084 

7093 

7101 

7110 

7118 

7126 

7*35 

7*43 

7*52 

52 

7160 

7168 

7177 

7185 

7i93 

7202 

7210 

7218 

7226 

7235 

53 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

7308 

73i6 

54 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388 

7396 

No. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

TABLES   AND   CHARTS 


331 


LOGARITHMS 


No. 

o 

i 

2 

3 

4 

5 

6 

7 

8 

9 

55 

7404 

7412 

7419 

7427 

7435 

7443 

7451 

7459 

7466 

7474 

56 

7482 

7490 

7497 

7505 

75i3 

7520 

7528 

7536 

7543 

755i 

57 

7559 

7566 

7574 

7582 

7589 

7597 

7604 

7612 

7619 

7627 

58 

7634 

7642 

7649 

7657 

7664 

7672 

7679 

7686 

7694 

7701 

59 

7709 

7716 

7723 

773i 

7738 

7745 

7752 

7760 

7767 

7774 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7846 

61 

7853 

7860 

7868 

7875 

7882 

7889 

7896 

7903 

7910 

7917 

62 

7924 

793  1 

7938 

7945 

7952 

7959 

7966 

7973 

7980 

7987 

63 

7993 

8000 

8007 

8014 

8021 

8028 

8035 

8041 

8048 

8055 

64 

8062 

8069 

8075 

8082 

8089 

8096 

8102 

8109 

8116 

8122 

65 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182 

8189 

66 

8i95 

8202 

8209 

8215 

8222 

8228 

8235 

8241 

8248 

8254 

67 

8261 

8267 

8274 

8280 

8287 

8293 

8299 

8306 

8312 

8319 

68 

8325 

8331 

8338 

8344 

835i 

8357 

8363 

8370 

8376 

8382 

69 

8388 

8395 

8401 

8407 

8414 

8420 

8426 

8432 

8439 

8445 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

7i 

8513 

8519 

8525 

853i 

8537 

8543 

8549 

8555 

8561 

8567 

72 

8573 

8579 

8585 

859i 

8597 

8603 

8609 

8615 

8621 

8627 

73 

8633 

8639 

8645 

8651 

8657 

8663 

8669 

8675 

8681 

8686 

74 

8692 

8698 

8704 

8710 

8716 

8722 

8727 

8733 

8739 

8745 

75 

875i 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797 

8802 

76 

8808 

8814 

8820 

8825 

8831 

8837 

8842 

8848 

8854 

8859 

77 

8865 

8871 

8876 

8882 

8887 

8893 

8899 

8904 

8910 

8915 

78 

8921 

8927 

8932 

8938 

8943 

8949 

8954 

8960 

8965 

8971 

79 

8976 

8982 

8987 

8993 

8998 

9004 

9009 

9oj  5 

9020 

9025 

80 

9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074 

9079 

81 

9085 

9090 

9096 

9101 

9106 

9112 

9117 

9122 

9128 

9i33 

82 

9138 

9T43 

9149 

9154 

9i59 

9*65 

9170 

9i75 

9180 

9186 

83 

9191 

9196 

9201 

9206 

9212 

9217 

9222 

9227 

9232 

9238 

84 

9243 

9248 

9253 

9258 

9263 

9269 

9274 

9279 

9284 

9289 

85 

9294 

9299 

93°4 

9309 

93i5 

9320 

9325 

9330 

9335 

9340 

86 

9345 

9350 

9355 

9360 

9365 

937° 

9375 

9380 

9385 

939° 

87 

9395 

9400 

9405 

9410 

94i5 

9420 

9425 

943° 

9435 

9440 

88 

9445 

945° 

9455 

9460 

9465 

9469 

9474 

9479 

9484 

9489 

89 

9494 

9499 

9504 

9509 

95i3 

95i8 

9523 

9528 

9533 

9538 

90 

9542 

9547 

9552 

9557 

9562 

9566 

957i 

9576 

958i 

9586 

9i 

9590 

9595 

9600 

9605 

9609 

9614 

9619 

9624 

9628 

9633 

92 

9638 

9643 

9647 

9652 

9657 

9661 

9666 

9671 

9675 

9680 

93 

9685 

9689 

9694 

9699 

9703 

9708 

97J3 

9717 

9722 

9727 

94 

9731 

9736 

974i 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

95 

9777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814 

9818 

96 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859 

9863 

97 

9868 

9872 

9877 

9881 

9886 

9890 

9894 

9899 

9903 

9908 

98 

9912 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948 

9952 

99 

9956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

999  1 

9996 

N^ 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

332  SOLENOIDS 


COMPARISON  OF  MAGNETIC  AND   ELECTRIC  CIRCUIT 
RELATIONS 

MAGNETIC  ELECTRIC 

Magnetomotive  force  (£f}  Electromotive  force  (E) 

Reluctance  (£%)  Resistance  (R) 

Flux  (0)  Current  (/) 

jj  /  =- 

"  &>  R 

Intensity  of  field   or    magnetizing       _._  .  .  ,_  . 

,~rL  Difference  of  potential  (E\) 

force  ecu^ 


Induction  or  flux  density  (6B)  Current  density  (Id) 


Reluctivity,  specific  reluctance  (v)       Resistivity,  specific  resistance  (p) 

AR 


=  1T  p=  i, 

Permeance,    reciprocal    of    reluc-       Conductance,  reciprocal  of  resist- 
tance  (cP  )  ance  (G) 


Permeability,   specific    permeance,       Conductivity,  specific  conductance, 
reciprocal  of  reluctivity  (/t)  reciprocal  of  resistivity  (7) 

7  ~P~Zff 


TABLES   AND   CHARTS 


333 


1 

r^\O   to  rf  ro  N   w   o   ONOO   r^NO   to  Tf  ro  M    HH   o   ONOO   i^.vO   to 

II 

,1 

to  to  rooo    O    ONNO    QWOt-sOdOvOOwQl'^n^'tONN 

O    roO  OO    I-H    W    rf  NO    1^  OO  CO    ON  ON  ONCO  OO    r--NO    rf  ro  M    ON  r^ 
CM     w    O     ON  ONOO    t^NO    to  Tj-   ro  C4     P-C    O     ONCO    t^NO    to  T)-  ro  M     O 

w 
£ 

d  d  d  d  d  d  d  d  d  d  d  d  o"  d  d  d  o"  d  d  d  d  d  d 

OTAN. 

ON  O    "">  rONO    I^»  O    w    ro  ro  ONNO    "-1    •**•  O    ON  ONOO    rf  NO    rj-  to  O 
LOvO    *^"  O    ri    O    *^~  Cl    rj-  O    ON  el  CO  NO    t^  ON  Tj"  I-H    O    O    r-l    to  o 
to  T}~  T^"  LONO  CO    O    rONO    O    rooo    ci    r^  M    r^.  ro  ON  to  I-H   t^  ro  O 

K 

<! 

H 

U 

55 

«• 
H 

ci    ^"NO  CO    O    ro  to  r^.  o    ri    T}*  t^.  O    r^   tooo    O    rONO   O    rONO   O 
T^-  -^-  ^J-  -^-  to  to  to  to  NO  NO  NO  NO    t^**  t^  I^^.  t^OO  CO  CO    ON  ON  ON  O 

z. 

<: 

H 

o 

dddddddddddddddo'dddo'dd^ 

0 

en 

1 

5 

t~>.  r^NO   *1~  O   tooo    O   O   ONNO   M  NO  oo  oo   r~»  rooo   <-•    <-<   O   r-^.  HH 

w* 
z 

% 

S5 
& 

w 

dddddddddddddddo'do'ddddd 

u 

PH 
g 

II 

ro  -f-  tONO   r-^oo    ON  O   >-i    r>   ro  ^t-  to\o   r-^co    ON  O   >-<    w   ro  TJ-  to 

<; 

1 

a 

2 

< 

O    ONOO    r^vO    to  -r  ro  n    <->    O    ONOO    I--NO   to  TJ-  ro  r-1    w    O    ONOO 
ONCO  OOCOOOCOOOCOCOOOOO   t^t^t^-l^t^t^t^r^t^  t^NO  NO 

o  o 

O 
O 

3 

§ 

O  00    ^J*NO  NO    r-i   to  to  ro  t^^OO  NO   HM   ^t-  ro  ON  ro  ro  ^   ^^  r^*vO   d 

(i 

MOOOOOOOOOOOOOOOOOOOOOO 

l-l 

< 

O    O    roi-i    t^M   •^•ro^OO    rONO  NO  toco   <-<   TJ-ONI^N   io«    M 

O    "^  rOOO    O    ro  •—  '    ^J*  **    >-H    t^>-  "^"  O    ro  >—  '    rOOO    r^  t^  d    Tt"  O    t^- 
O   r-i  NO   O    ro  ~^t"  to  i—  i    HH    roNO   *—  '   t^.  ro  O   t^>.  ^*  c^   o   ON  r^NO   TJ~ 

i 

U 

O   t^-oo    ON  "*t*  i^    ONOO   t"^NO   *-o  to  T^-  ^-  -^  ro  ro  ro  ro  c^   ci   d   d 

H 

Z 

< 

§i^-  —?•  ci    ^\  t^  ^o  c-i    O  CO  NO    "^  r-j    O    0s  r^NO   ly^  ^~  ^  ^f  ro  "^f 
-H    ro  tONO  CO    O    <M    -<ttot^ONi-H    ro  rfNO  OO    O    W    ^'O  OO    O 
OOOOOOHHwhHhHMhHWMocicjrororororo^- 

i 

dodo  d  dddddddddd  odd  o'd  odd 

° 

M 
£ 

O    to  O\  rooO    ri    to  ON  rj    'tO  CO    ON  O    ONOO  NO    •**•  O  VO    O    T}-NO 

M 

ddddddddddddddddddddddd 

0 

00 

Q    M    C^    CO  ^f  ^-O^O    Is**  OO    ON  O    t—1    M    **O  ^t*  *-O^O    t^*CO    ON  O    ^^    ^ 

0 

<Q 

<J 

INDEX 


Absolute  units,  2. 
Action,  rapid,  slow,  184. 
Active  pressure,  157. 
Activity,  237-245. 
Advance  wire,  218. 
Aging  of  magnets,  12. 
Air-core,  76-78. 
Air-gap,  10,  33,  113,  119. 
Air,  permeability  of,  104. 
Alternating-current  (A.  C.), 

electromagnet  calculations,  175. 

electromagnets,  168. 

horseshoe  electromagnet,  174. 

iron-clad  solenoid,  171. 

plunger  electromagnet,  172. 

solenoid,  168. 

windings,  181. 
Alternating  currents,  154. 

e.  m.  f.,  155. 
Alternation,  155. 
American  wire  gauge,  215. 
Ampere,  17. 
Ampere-turn,  27. 

Ampere-turns,  68,  79,  142,  239,  246, 
248. 

per  centimeter  length,  34,  68. 
Angles,  121,  123. 
Angular  velocity,  159. 
Annealing,  192. 
Area, 

of  plunger,  77,  79,  83,  108. 

polar,  114,  120. 
Armature,  14,  132,  133. 
Armatures,  external,  131. 
Artificial  magnet,  8,  10. 
Asbestos,  221. 
Attraction,  25,  41,  76, 142. 

mutual,  41. 
Average  radius,  65. 


Back  iron,  133. 

Baker,  H.  S.,  32. 

Bar  electromagnet,  132. 

Bar  permanent  magnet,  13,  64. 

Billet  magnet,  137. 

Bobbins,  195. 

British  thermal  unit,  296. 

Bulging  of  lines,  113. 


Calorie,  296. 

Capacity,  160, 162. 

Carichoff,  E.  R.,  113,  120. 

Carrying  capacity  of  wires,  219. 

Cast  iron,  191. 

Cast  steel,  191. 

Centigrade  scale,  297. 

Centimeter,  2,  3,  15. 

C.  G.  S.  system,  2. 

Circles  of  force,  25. 

Circuit, 

electric,  17,  27,  153. 

magnetic,  9,  27,  34,  76,  153. 

return,  15, 102,  111. 

shunt,  20. 

Circular  winding,  257. 
Climax  wire,  218. 
Closed-ring  magnet,  9. 
Coefficient, 

leakage,  37. 

of  self-induction,  149. 

temperature,  19,  210. 
Coercive  force,  12. 
Coil-and-plunger,  41. 
Coil,  coils, 

dimensions  of,  55,  56,  71 ,  108. 

exciting,  126. 


335 


336 


INDEX 


Coil,  coils — Continued. 

insulation  of,  201. 

neutralizing,  128. 

operating,  126. 

resistance,  277. 

retaining,  126. 

thermal,  302. 
Collar  on  plunger,  130. 
Common  systems  of  units,  3. 
Compass  needle,  14,  24. 
Compound  magnet,  15. 
Condenser,  160,  186. 
Conductance,  17. 

joint,  21. 

specific,  19. 
Conductivity,  19,  242. 
Conductor,  electric,  18,  20,  40,  211. 
Coned  plungers,  120,  125. 
Connections, 

multiple  (parallel),  20,  286. 

series,  20,  286. 
Consequent  poles,  14. 
Constant  reluctance,  122. 
Construction  of  solenoid,  82. 
Conversions  of  units,  7. 
Copper  wire,  219,  305. 
Core,  cores, 

air,  76,  77,  78. 

iron,  77,  78. 

laminated  (subdivided),  153,  171. 

rectangular,  260. 

round,  257,  263. 

square,  260,  263. 
Cotton,  220. 
Counter- e.  m.  f.,  22. 
Current,  currents,  17. 

alternating,  154. 

density  of,  18. 

eddy,  153. 

effective,  159. 

in  opposition,  164. 

in  quadrature,  164. 

maximum,  159. 
Curve, 

magnetization,  29. 

permeability,  28. 

pull,  93. 

saturation,  31. 
Cushion,  magnetic,  107. 
Cycle,  155. 


D 

Deltabeston  wire,  225,  313. 
Density, 

flux,  16,  29,  112,  113,  127. 

of  current,  18. 

practical  working,  30. 
Design  of    plunger  electromagnets, 

129. 
Diameter  of, 

plunger,  82,  84. 

solenoid,  82. 

winding,  257. 

wire,  215,  254,  256,  283. 
Difference  of  potential,  17. 
Differentia]  winding,  277. 
Dimensions  of, 

coils,  55,  56,  71, 108. 

plungers,  70,  108. 
Disk, 

solenoid,  50. 

solenoids,  tests  of,  54. 

winding,  50,  273. 
Distortion  of  field,  26. 
Drop,  22. 
Dyne,  2,  15,  16. 


Earth's  magnetism,  25. 
Eddy  currents,  153,  181. 
Effective, 

current,  159. 

e.  in.  f.  or  pressure,  155. 

work,  1. 
Efficiency,  2. 
Electric,  electrical, 

circuit,  17,  27,  153. 

conductor,  18,  20,  40. 

energy,  18,  149. 

inertia,  151. 

power,  18. 

pressure,  17. 

units,  17. 

Electricity,  17,  27. 

Electromagnet,   electromagnets,  28, 
133. 

alternating-current,  168. 

bar,  132. 

iron-clad,  136.^ 


INDEX 


337 


Electromagnets  —  Continued. 

lifting,  137. 

plunger,  110. 

polarity  of,  144. 

polarized,  144. 

polyphase,  176. 

ring,  133. 

round-core,  265. 

square-core,  265. 
Electromagnetic, 

phenomena,  148. 

windings,  229. 
Electromaguetism,  24. 
Electromotive  force  (e.  m.  f.),  17, 
155. 

active,  157. 

alternating,  155. 

average,  155. 

effective,  155. 

impressed,  156. 

maximum,  155. 

resultant,  157. 

self-induction,  156,  157. 
Enameled  wire,  221,  312. 
Energy,  1. 

electric,  18. 

magnetic,  149. 
English  system  of  units,  3. 
Erg,  3. 
Ether,  9. 

Exc-iting  coils,  126. 
External, 

armatures,  131. 

reluctance,  77. 

resistance,  21. 


Fahrenheit  scale,  297. 

Farad,  161. 

Ferric  materials,  191. 

Ferro-nickel  wire,  218. 

Fiber,  193. 

Field, 

distortion  of,  26. 

intensity  of  magnetic,  16. 

magnetic,  24,  149. 

magnets,  12. 

of  force,  9. 
Filings,  iron,  62. 


Flux,  33. 

density,  16,  29, 112,  113,  127. 

magnetic,  16. 

paths,  123. 
Flux-turns,  149,  159. 
Foot-pound,  3. 
Force,  1. 

at  center  of  square  winding,  54. 

circles  of,  25. 

coercive,  12. 

due  to  circular  current,  26. 

due  to  several  disks,  51. 

due  to  several  turns,  45,  49. 

due  to  single  turn,  42. 

electromotive,  17. 

field  of,  9. 

lines  of,  9. 

magnetic,  8. 

magnetizing,  25,  32,  65. 

magnetomotive,  32,  33. 

unit,  15. 

Forces,  sum  of,  45. 
Forms  of  plunger  electromagnets,  129. 
Frame,  iron,  102,  112. 
Frames,  129. 
Frequency,  155. 
Friction,  80. 
Fundamental  units,  2. 


G 

Gauss,  16. 

Gilbert,  32. 

Goldsborough,  W.  E.,  124. 

Gram,  grams,  2,  3,  76. 

Graphite,  18(5. 

Gravity,  3. 

Groups  of  terms,  47. 

H 

Hard  rubber,  192. 
Heat, 

mechanical  equivalent  of,  296. 

specific,  296. 

units,  29(5. 

Heating  of  coils,  298. 
Helix,  40. 

Helmholtz-'s  law,  151. 
Henry,  149. 


338 


INDEX 


Horseshoe  electromagnet,  133. 

A.  C.,  174. 

test  of,  134. 

Horseshoe  permanent  magnet,  14. 
Horse  power,  18. 
Hysteresis,  165. 

loop,  166. 

loss,  166. 
Hysteretic  constant,  166. 


Imbedding  of  wires,  232. 

Impedance,  160. 

Impressed  pressure   (e.  m.  f.),   156, 

157. 
Inductance,  140,  151,  162. 

coil,  169. 

of  solenoid,  152. 
Induction,  148,  176. 

magnetic,  15,  16. 

self,  149,  150,  160. 
Inductive  reactance,  160. 
Inertia,  electrical,  151. 
Ingot  magnet,  137. 
Insulated  wire  (wires),  220,  309. 

notation  for,  226. 

Insulating  materials,  193,  220,  325. 
Insulation, 

external,  201. 

internal,  201. 

of  coils,  201. 

temperature-resisting  qualities  of, 
222. 

thickness,  228,  256. 
Intensity  of  magnetic  field,  16,  76. 

of  magnetization,  15. 
Internal, 

diameter  of  solenoids,  82. 

reluctance,  77. 

resistance,  21. 
Iron,  8,  9. 

cast,  191. 

core,  77,  78. 

filings,  10,  62. 

frame,  102,  112. 

soft,  10,  12. 

Swedish,  70,  191. 

wrought,  77,  191. 


Iron-clad, 

electromagnet,  136. 
solenoid,  102,  104. 
solenoid  (A.  C.),  171. 


Joint, 

conductance,  21. 

resistance,  20,  280. 
Joints,  36. 
Joule,  18,  296. 
Joule's  equivalent,  296, 

K 

Kilo  ampere-turns,  72. 
Kilogram,  3,  76. 
Kilometer,  3. 
Kilowatt,  18. 


Laminated  core,  171. 
Law, 

Helmholtz's,  151. 

of  magnetic  circuit,  32. 

Ohm's,  17. 

Lenz's,  148. 
Leakage,  39,  112,  132. 

coefficient,  37. 

magnetic,  28,  36, 127. 

paths,  :!<). 
Length,  2. 

of  plunger,  70,  88,  102. 

of  solenoid,  69,  85. 

of  stop,  101. 

of  wire,  213,  251. 
Lenz's  law,  148. 
Lifting  magnets,  137. 
Limbs  of  magnet,  132. 
Limit  of  magnetization,  29. 
Lines  of  force,  9. 

bulging  of,  113. 
Lodestone,  8. 
Logarithms,  330. 

M 

Magnet,  magnets,  8. 
aging  of,  12. 
artificial,  8,  10. 
billet,  137. 


INDEX 


339 


Magnet,  magnets  —  Continued. 

closed-ring,  9. 

compound,  15. 

field,  12. 

ingot,  137. 

lifting,  137. 

permanent,  10,  12. 

plate,  137. 

valve,  125. 

wire,  210. 
Magnetic, 

circuit,  9,  27,  32,  34,  7G,  153. 

cushion,  107. 

energy,  149. 

field,  24,  149. 

field,  intensity  of,  1C,  76. 

field  of  solenoids,  61. 

rlux,  1G. 

force,  8. 

induction,  15,  10. 

leakage,  28,  ;5G,  127. 

moment,  15. 

permeability,  10. 

pole,  12. 

pole,  unit,  10. 

resistance,  10. 

substance,  8,  9. 

units,  15. 
Magnetism,  8,  13,  27. 

earth's,  25. 

residual,  12. 
Magnetization , 

curve,  29. 

intensity  of,  15. 

limit  of,  29. 

Magnetizing  force,  25,  32,  65. 
Magnetomotive  force  (in.  m.  f.),  32, 

^33,  68. 

Manganin  wire,  219,  317. 
Mass,  2. 
Materials, 

ferric,  191. 

insulating,  193,  220. 
Maximum, 

current,  159. 

pull,  71,  75. 

pull,  position  of,  70,  119. 
Maxwell,  16. 
Maxwell's  formula,  153. 
Mean  magnetic  radius,  50. 


Mechanical  equivalent  of  heat,  296. 

Meter,  3. 

Metric  wire  table,  217,  306. 

Mho,  17. 

Microfarad,  101. 

Mil,  225. 

Mil-increase,  225. 

Millimeter,  3. 

Minimum  expenditure  in  watts,  83. 

Moment,  magnetic,  15. 

Monel  wire,  321. 

Multiple-coil  winding,  188,  197,  277. 

Multiple  connection,  20,  286. 

Multiple-wire  winding,  188,  274. 

Mutual  attraction,  4. 

N 

Nachod,  C.  P.,  125. 
Neutral  point,  13. 
Neutralizing  coil,  128. 
Nichrome  wire,  219,  318. 
Non-inductive  winding,  277. 
Notation, 

for  bare  wires,  212. 

for  isulated  wires,  226. 

in  powers  of  ten,  7. 

O 

Oersted,  16. 

Ohm,  17. 

Ohm's  law,  17. 

Ohms  per  cubic  inch,  252,  283. 

Operating  coil,  1'JO. 


Paper  between  layers,  272. 
Parallel  connections,  20,  286. 
Percentage  of  maximum  pull,  96. 
Period,  155. 

Permanent    magnet   (magnets),   10, 
12,  13. 

bar,  13,  14. 

horseshoe,  14. 

practical,  14. 
Permeability, 

curve,  28. 

magnetic,  16,  28,  33,  76,  83,  323. 

of  air,  104. 


340 


INDEX 


Permeances,  36. 
Phase,  157,  164. 
Pitch  of  turns,  234. 
Plate  magnet,  137. 
Plunger,  plungers,  41,  63. 

area  of,  77,  79,  83,  108. 

coned,  120,  125. 

diameter  of  ,82,  84. 

dimensions  of,  70,  108. 

electromagnet,  110.  v 

electromagnet  (A.  C.),  172. 

electromagnet,  design  of,  129. 

electromagnet,  pushing,  130. 

length  of,  70,  88,  102. 

pointed,  98,  123. 

weight  of,  70,  80,  123. 

with  collar,  130. 
Pointed  plungers,  98,  123. 
Polar  area,  114,  120. 
Polarity,  13. 

of  electromagnets,  144. 

of  loop,  25. 

of  magnet,  25. 

Polarized  electromagnets,  144. 
Pole,  poles,  13. 

consequent,  14. 

like,  13. 

magnetic,  12. 

north,  12. 

north-seeking,  12. 

theoretical,  13. 

unit,  magnetic,  13,  16. 

unit,  strength  of,  15. 

unlike,  13. 
Polyphase, 

electromagnets,  176. 

systems,  164. 
Position  of, 

gap, 119. 

maximum  pull,  76,  78,  119. 
Potential,  difference  of,  17. 
Power,  1. 

electric,  18. 

horse,  18. 

mechanical  unit  of,  3. 
Practical, 

solenoids,  45. 

working  densities,  30. 
Predominating  pull,  110. 
Prefixes  in  C.  G.  S.  system,  3. 


Pressure  or  e.  m.  f.,  155. 

active,  157. 

average,  155. 

effective,  155,  156. 

electric,  17. 

impressed,  157. 

local,  162. 

maximum,  155. 

resultant,  157. 

self-induced,  156. 

self-induction,  157. 
Pull,  3,  57,  76,  85,  88,  104,  111,  113, 
142. 

curve,  93.  \ 

due  to  solenoid,  58. 

maximum,  71,  75. 

percentage  of  maximum,  96. 

position  of  maximum,  76. 

predominating,  110. 
Pushing  plunger  electromagnet,  130. 


R 

Radius, 

average,  65. 

mean  magnetic,  50. 
Range,  88,  103,  105,  112. 
Rapid  action,  184. 
Reactance,  inductive,  160. 
Rectangular, 

cores,  260. 

wires,  217. 

Reluctance,  16,  33,  76,  78,  104,   111, 
112. 

between  cylinders,  38. 

between  flat  surfaces,  37. 

constant,  122. 

external,  77. 

internal,  77. 

specific  magnetic,  16. 
Reluctivity,  16. 
Repulsion,  25,  41. 
Residual  magnetism,  12. 
Resistance,  1,  157,  160,  186,  246,  251, 
255,  269. 

coils,  277. 

external,  21. 

internal,  21. 

joint,  20,  280. 

non-inductive,  155. 


INDEX 


341 


Resistance  —  Continued. 

specific,  19,  120. 

wires,  213,  218. 
Resistivity,  18,  210. 
Resonance,  161. 

Resultant  pressure  or  e.  m.  f.,  157. 
Retaining  coil,  120. 
Retentiveness,  12. 
Return  circuit,  15,  102,  111. 
Ribbon,  217. 

winding,  273. 

Rim  solenoids,  tests  of,  54. 
Ring  electromagnet,  133. 
Rise  in  temperature,  18,  80. 
Round-core  electromagnet,  265. 
Round  wire,  211,  230. 
Rowland,  Professor,  296. 
Rubber,  hard,  192. 


S 

Saturation, 

curve,  31. 

point,  29,  30,  78. 
S.  B.  wire,  219,  317. 
Second,  2. 

Self-induced  pressure  or  e.  m.  f.,  156. 
Self-induction,  149,  150,  160. 

coefficient  of,  156. 

e.  m.  f.  or  pressure,  157. 
Series  connections,  20,  286. 
Short-circuited  winding,  184. 
Shunt  circuit,  20. 
Silk,  221. 

Silk-insulated  wires,  225. 
Simple  solenoid,  76. 
Sine  curve  (sinusoid),  155. 
Skull-cracker,  137. 
Slow  action,  184. 
Solenoid,  solenoids,  40,  64,  76,  168. 

construction  of,  82. 

diameter  of,  82. 

disk,  50. 

inductance  of,  152. 

iron-clad,  102,  104. 

length  of,  69,  85. 

magnetic  field  of,  61. 

practical,  45. 

pull  due  to,  58. 

simple,  76. 


Solenoid,  solenoids — Continued. 

stopped,  99. 

tests  of,  69. 

tests  of  rim  and  disk,  54. 

total  work  due  to,  82. 
Sparking,  185. 
Specific, 

conductance,  19. 

heat,  296. 

magnetic  reluctance,  16. 

resistance,  19,  210. 
Square-core, 

electromagnet,  265. 

winding,  52. 

winding,  force  at  center  of,  54. 

wire,  217,  230. 
Square  cores,  260,  263. 
Squeezing,  271. 
Steel,  8,  9. 

cast,  191. 

frame,  105. 

hardened, 10,  12. 

soft,  10. 
Steinmetz,  166. 
Sticking,  189. 
Stop,  99,  110. 

length  of,  101. 
Stopped  solenoid,  99. 
Stranded  conductor,  211. 
Subdivided  core,  153. 
Sum  of  forces,  45. 
Swedish  iron,  70,  191. 


Temperature, 

coefficient,  19,  210. 

resisting  qualities    of    insulation, 
222. 

rise  in,  18,  80. 
Tension,  270. 
Terminals,  197. 
Tests  of, 

disk  solenoids,  54. 

horseshoe  electromagnet,  134. 

practical  solenoids,  69. 

rim  solenoids,  54. 
Thermal, 

coils,  302. 

unit,  British,  296. 
Thermometers,  297. 


342 


INDEX 


Thickness  of  insulation,  228. 
Thompson,  Professor  S.  P.,  188. 
Three-phase  system,  164. 
Time,  1,  2. 

constant,  150,  188. 
Total  work  due  to  solenoid,  87. 
Turn,  turns,  253,  269. 

ampere,  239,  246,  248. 

flux,  149,  159. 

groups  of,  47. 

pitch  of,  234. 
Two-phase  system,  164. 

U 

Unit,  units, 
absolute,  2. 
British  thermal,  296. 
C.  G.  S.,  2. 
distance,  15. 
electric,  17. 
English,  3. 
force,  15. 
fundamental,  2. 
heat,  296. 
magnetic,  15. 
magnetic  pole,  13,  16. 
relations  between,  3. 
strength  of  pole,  15. 


Valve  magnet,  125,  130. 

Volt,  17. 

Volts, 

per  layer,  241. 

per  turn,  240. 

W 

Watt,  watts,  18,  239,  248. 

minimum  expenditure,  83. 
Watt-second,  290. 
Weight  of, 

copper  wire,  212. 

plunger,  70,  80. 

wire,  213,  254,  255. 
Whistle  valve  magnet,  130. 


Winding,  windings, 

alternating  current,  181. 

circular,  257. 

diameter  of,  257. 

differential,  274,  277. 

disk,  50,  273. 

electromagnetic,  229. 

in  series  with  resistance,  287. 

multiple-coil,  188,  197,  277. 

multiple-wire,  188,  274. 

non-inductive,  277. 

ribbon,  273. 

short-circuited,  184. 

square,  52,  260. 
Wire,  wires, 

Advance,  219,  320. 

Climax,  219,  319. 

Copper,  219. 

Deltabeston,  225. 

diameter  of,  215,  254,  256. 

enameled,  221. 

ferro-nickel,  219,  317. 

gauge,  American,  215. 

imbedding  of,  232. 

insulated,  220. 

length  of,  213,  251. 

magnet,  210. 

Manganin,  219,  317. 

Monel,  321. 

Nichrome,  219,  318. 

notation  for  bare,  212. 

notation  for  insulated,  226. 

rectangular,  217. 

resistance,  218,  317. 

resistance  of,  213. 

round,  211,  230. 

S.  B.,  219,  317. 

square,  217,  230. 

tables,  216,  304,  322. 

weight  of,  212,  213,  254,  255. 
Work,  1. 

absolute  unit  of,  3. 

due  to  solenoids,  82. 

mechanical  unit  of,  3. 
Wrought  iron,  77,  191. 


Yoke,  38,  133. 


Of    THf 

UNIVERSITY 


LIST  OF  WORKS 

ELECTRICAL    SCIENCE 

PUBLISHED   AND   FOR    SALE   BY 

D.    VAN   NOSTRAND  COMPANY, 

23  Murray  and  27  Warren  Streets,  New  York. 


ABBOTT,  A.  V.  The  Electrical  Transmission  of  Energy.  A  Manual  for 
the  Design  of  Electrical  Circuits.  Fifth  Edition,  enlarged  and  rewritten. 
With  many  Diagrams,  Engravings  and  Folding  Plates.  8vo.,  cloth, 
675  pp Net,  $5 .00 

ADDYMAN,  F.  T.  Practical  X-Ray  Work.  Illustrated.  8vo.,  cloth,  200 
pp.  . .. Net,  $4.00 

ALEXANDER,  J.  H.  Elementary  Electrical  Engineering  in  Theory  and 
Practice.  A  class-book  for  junior  and  senior  students  and  working 
electricians.  Illustrated.  12mo.,  cloth,  208  pp $2.00 

ANDERSON,  GEO.  L.,  A.M.  (Capt.  U.S.A.).     Handbook  for  the  Use  of 

•Electricians  in  the  operation  and  care  of  Electrical  Machinery  and 

Apparatus  of  the  United  States  Seacoast  Defenses.     Prepared  under 

the  direction  of  Lieut. -General  Commanding  the  Army.     Illustrated. 

8vo.,  cloth,  16X  pp $3.00 

ARNOLD,  E.  Armature  Windings  of  Direct-Current  Dynamos.  Exten- 
sion and  Application  of  a  general  Winding  Rule.  Translated  from 
the  original  German  by  Francis  B.  DeGress.  Illustrated.  8vo., 
cloth,  124  pp $2.00 


ASHE,  S.  W.,  and  KEILEY,  J.  D.  Electric  Railways  Theoretically  and 
Practically  Treated.  Illustrated.  12mo.,  cloth. 

Vol.  I.     Rolling  Stock.     Second  Edition.     285  pp Net,  $2 . 50 

Vol.  II.     Substations  and  Distributing  Systems.     296  pp.  ..  .Net,  $2.50 

ATKINSON,  A.  A.,  Prof.  (Ohio  Univ.).  Electrical  and  Magnetic  Calcula- 
tions. For  the  use  of  Electrical  Engineers  and  others  interested  in 
the  Theory  and  Application  of  Electricity  and  Magnetism.  Third 
Edition,  revised.  Illustrated.  8vo.,  cloth,  310  pp Net,  $1 . 50 

—  PHILIP.     The   Elements    of   Dynamic    Electricity   and   Magnetism. 
Fourth  Edition.     Illustrated.     12mo.,  cloth,  405  pp $2.00 

Elements  of  Electric  Lighting,  including  Electric  Generation,  Measure- 
ment, Storage,  and  Distribution.  Tenth  Edition,  fully  revised  and  new 
matter  added.  Illustrated.  12mo.,  cloth,  280  pp $1 .50 

Power  Transmitted  by  Electricity  and  Applied  by  the  Electric  Motor, 

including  Electric  Railway  Construction.    Illustrated.   Fourth  Edition, 

fully  revised  and  new  matter  added.     12mo.,  cloth,  241  pp.    .  .$2.00 

AYRTON,  HERTHA.     The  Electric  Arc.     Illustrated.     8vo.,   cloth,   479 

pp Net,  $5.00 

—  W.  E.     Practical  Electricity.     A  Laboratory  and   Lecture  Course. 
Illustrated.     12mo.,  cloth,  643  pp $2.00 

BIGGS,  C.  H.  W.  First  Principles  of  Electricity  and  Magnetism.  Illus- 
trated. 12mo.,  cloth,  495  pp $2 .00 

BONNEY,  G.  E.  The  Electro-Plater's  Hand  Book.  A  Manual  for  Ama- 
teurs and  Young  Students  of  Electro-Metallurgy.  Fourth  Edition, 
enlarged.  61  Illustrations.  12mo.,  cloth,  208  pp $1 .20 

BOTTONE,  S.  R.  Magnetos  For  Automobilists ;  How  Made  and  How  Used. 
A  handbook  of  practical  instruction  on  the  manufacture  ancl  adapta- 
tion of  the  magneto  to  the  needs  of  the  motorist.  Illustrated.  12mo., 

cloth,  88  pp Net,  $1 .00 

Electric  Bells  and  All  about  Them.  12mo.,  cloth 50  cents 

Electrical  Instrument-Making  for  Amateurs.  A  Practical  Handbook. 
Enlarged  by  a  chapter  on  "The  Telephone."  Sixth  Edition.  With 

48  Illustrations.  12mo.,  cloth 50  cents 

Electric  Motors,  How  Made  and  How  Used.  Illustrated.  12mo.,  cloth, 
168  pp 75  cents 

BOWKER,  WM.  R.  Dynamo,  Motor,  and  Switchboard  Circuits  for  Elec- 
trical Engineers:  a  practical  book  dealing  with  the  subject  of  Direct, 
Alternating,  and  Polyphase  Currents.  With  over  100  Diagrams  and 
Engravings.  8vo.,  cloth,  120  pp Net,  $2.25 


BUBIER,  E.  T.  Questions  and  Answers  about  Electricity.  A  First  Book 
for  Beginners.  12mo.,  cloth 50  cents 

CARTER,  E.  T.  Motive  Power  and  Gearing  for  Electrical  Machinery;  a 
treatise  on  the  theory  and  practice  of  the  mechanical  equipment  of 
power  stations  for  electric  supply  and  for  electric  traction.  Second 
Edition,  revised.  Illustrated.  8vo.,  cloth,  700  pp Net,  $5.00 

CHILD,  CHAS.  T.  The  How  and  Why  of  Electricity :  a  book  of  informa- 
tion for  non-technical  readers,  treating  of  the  properties  of  Elec- 
tricity, and  how  it  is  generated,  handled,  controlled,  measured,  and 
set  to  work.  Also  explaining  the  operation  of  Electrical  Apparatus. 
Illustrated.  8vo.,  cloth,  140  pp $1 .00 

CLARK,  D.  K.  Tramways,  Their  Construction  and  Working.  Second 
Edition.  Illustrated.  8vo.,  cloth,  758  pp $9.00 

COOPER,  W.  R.     Primary  Batteries:    their  Theory,  Construction,  and  Use. 

131  Illustrations.     8vo.,  cloth,  324  pp Net,  $4.00 

The  Electrician  Primers.  Being  a  series  of  helpful  primers  on  electrical 
subjects,  for  use  of  students,  artisans,  and  general  readers.  Second 
Edition.  Illustrated.  Three  volumes  in  one.  8vo.,  cloth.  .  Net,  $5.00 

Vol.  I.— Theory Net,  $2 .00 

Vol.  II.— Electric  Traction,  Lighting  and  Power Net,  $3.00 

Vol.  III.— Telegraphy,  Telephony,  etc Net,  $2 . 00 

CROCKER,  F.  B.  Electric  Lighting.  A  Practical  Exposition  of  the  Art 
for  the  use  of  Electricians,  Students,  and  others  interested  in  the 
Installation  or  Operation  of  Electric- Lighting  Plants. 

Vol.  I. — The  Generating  Plant.  Seventh  Edition,  entirely  revised.  Illus- 
trated. 8vo.,  cloth,  482  pp $3 .00 

Vol.  II. — Distributing  System  and  Lamps.  Sixth  Edition.  Illustrated. 
8vo.,  cloth,  505  pp $3 . 00 

and   ARENDT,   M.     Electric    Motors :    Their   Action,    Control,   and 

Application.     Illustrated.     8vo.,  cloth In  Press 

and  WHEELER,  S.  S.     The  Management  of  Electrical  Machinery. 

Being  a  thoroughly  revised  and  rewritten  edition  of  the  authors'  "  Prac- 
tical Management  of  Dynamos  and  Motors."  Seventh  Edition. 
Illustrated.  16mo.,  cloth,  232  pp Net,  $1 .00 

CUSHING,  H.  C.,  Jr.  Standard  Wiring  for  Electric  Light  and  Power. 
Illustrated.  16mo.,  leather,  156  pp $1 .00 

DAVIES,  F.  H.  Electric  Power  and  Traction.  Illustrated.  8vo.,  cloth, 
293  pp.  (Van  Nostrand's  Westminster  Series.) Net,  $2 .00 


DIBDIN,  W.  J.  Public  Lighting  by  Gas  and  Electricity.  With  many  Tables, 
Figures,  and  Diagrams.  Illustrated.  8vo.,  cloth,  537  pp.Net,  $8.00 

DINGER,  Lieut.  H.  C.  Handbook  for  the  Care  and  Operation  of  Naval 
Machinery.  Second  Edition.  124  Illustrations.  16mo.,  cloth, 
302  pp Net,  $2.00 

DYNAMIC  ELECTRICITY:  Its  Modern  Use  and  Measurement,  chiefly 
in  its  application  to  Electric  Lighting  and  Telegraphy,  including: 
1.  Some  Points  in  Electric  Lighting,  by  Dr.  John  Hopkinson.  2.  On 
the  Treatment  of  Electricity  for  Commercial  Purposes,  by  J.  N.  Shool- 
bred.  3.  Electric-Light  Arithmetic,  by  R.  E.  Day,  M.E.  Fourth 
Edition.  Illustrated.  16mo.,  boards,  166  pp.  (No.  71  Van  Nos- 
trand's  Science  Series.) 50  cents 

EDGCUMBE,  K.  Industrial  Electrical  Measuring  Instruments.  Illus- 
trated. 8vo.,  cloth,  227  pp Net,  $2.50 

ERSKINE-MURRAY,  J.  A  Handbook  of  Wireless  Telegraphy :  Its  Theory 
and  Practice.  For  the  use  of  electrical  engineers,  students,  and 
operators.  Illustrated.  8vo.,  cloth,  320  pp Net,  $3 .50 

EWING,  J.  A.  Magnetic  Induction  in  Iron  and  other  Metals.  Third 
Edition,  revised.  Illustrated.  8vo.,  cloth.  393  pp Net,  $4.00 

FISHER,  H.  K.  C.,  and  DARBY,  W.  C.  Students'  Guide  to  Submarine  Cable 
Testing.  Third  Edition,  new,  enlarged.  Illustrated.  8vo.,  cloth, 
326 pp Net,  $3.50 

FLEMING,  J.  A.,  Prof.  The  Alternate-Current  Transformer  in  Theory 
and  Practice. 

Vol.  I.:  The  Induction  of  Electric  Currents.  Fifth  Issue.  Illustrated. 
8vo.,  cloth,  641  pp , Net,  $5 . 00 

Vol.  II. :  The  Utilization  of  Induced  Currents.  Third  Issue.  Illus- 
trated. 8vo.,  cloth,  587  pp Net,  $5.00 

Handbook  for  the  Electrical  Laboratory  ?.nd  Testing  Room.  Two  Vol- 
umes. Illustrated.  8vo..  cloth,  1160  pp.  Each  vol Net,  $5.00 

FOSTER,  H.  A.  With  the  Collaboration  of  Eminent  Specialists.  Electri- 
cal Engineers'  Pocket  Book.  A  handbook  of  useful  data  for  Elec- 
tricians and  Electrical  Engineers.  With  innumerable  Tables,  Dia- 
grams, arid  Figures.  The  most  complete  book  of  its  kind  ever  pub- 
lished, treating  of  the  latest  and  best  Practice  in  Electrical  Engineer- 
ing. Fifth  Edition,  completely  revised  and  enlarged.  Fully  Illustrated. 
Pocket  Size.  Leather.  Thumb  Indexed.  1636  pp $5.00 


GANT,  L.  W.  Elements  of  Electric  Traction  for  Motormen  and  Others. 
Illustrated  with  Diagrams.  8vo.,  cloth*  217  pp Net,  $2 .50 

GERHARDI,  C.  H.  W.  Electricity  Meters;  their  Construction  and  Man- 
agement. A  practical  manual  for  engineers  and  students.  Illus- 
trated. 8vo.,  cloth,  337  pp Net,  $4.00 

GORE,  GEORGE.  The  Art  of  Electrolytic  Separation  of  Metals  (Theoret- 
ical and  Practical).  Illustrated.  8vo.,  cloth,  295  pp Net,  $3 . 50 

GRAY,  J.  Electrical  Influence  Machines :  Their  Historical  Development 
and  Modern  Forms.  With  Instructions  for  making  them.  Second 
Edition,  revised  and  enlarged.  With  105  Figures  and  Diagrams. 
12mo.,  cloth,  296  pp $2 .00 

HAMMER,  W.  J.  Radium,  and  Other  Radio  Active  Substances;  Polo- 
nium, Actinium,  and  Thorium.  With  a  consideration  of  Phospho- 
rescent and  Fluorescent  Substances,  the  properties  and  applications 
of  Selenium,  and  the  treatment  of  disease  by  the  Ultra- Violet  Light. 
With  Engravings  and  Plates.  8vo.,  cloth,  72  pp $1 .00 

HARRISON,  N.  Electric  Wiring  Diagrams  and  Switchboards.  Illus- 
trated. 12mo.,  cloth,  272  pp $1 .50 

HASKINS,  C.  H.  The  Galvanometer  and  its  Uses.  A  Manual  for  Elec- 
tricians and  Students.  Fifth  Edition,  revised.  Illustrated.  16mo., 
morocco,  75  pp $1 . 50 

HAWKINS,  C.  C.,  and  WALLIS,  F.  The  Dynamo:  Its  Theory,  Design, 
and  Manufacture.  Fourth  Edition,  revised  and  enlarged.  1 90  Illustra- 
tions. 8vo.,  cloth,  925  pp $3.00 

HAY,  ALFRED.  Principles  of  Alternate-Current  Working.  Second  Edition. 
Illustrated.  12mo.,  cloth,  390  pp $2  00 

Alternating  Currents;  their  theory,  generation,  and  transformation. 
Second  Edition.  191  Illustrations.  8vo.,  cloth,  319pp.  .Net,  $2  50 

An  Introductory  Course  of  Continuous-Current  Engineering.  Illus- 
trated. 8vo.,  cloth,  327  pp Net  $2  50 

HEAVISIDE,  0.  Electromagnetic  Theory.  Two  Volumes  with  Many 
Diagrams.  8vo.,  cloth,  1006  pp.  Each  Vol Net,  $5  00 

HEDGES,   K.     Modem   Lightning   Conductors.     An   illustrated    Supple- 
ment to  the  Report  of  the  Research  Committee  of  1905,  with  notes 
as  to  methods  of  protection  and  specifications.     Illustrated      8vo 
cloth,  1 19  pp N 


HOBART,  H.  M.  Heavy  Electrical  Engineering.  Illustrated.  8vo., 
cloth,  307  pp t In  Press 

HOBBS,  W.  R.  P.  The  Arithmetic  of  Electrical  Measurements.  With 
numerous  examples,  fully  worked.  Twelfth  Edition.  12mo.,  cloth, 
126  pp 50  cents 

HOMANS,  J.  E.  A  B  C  of  the  Telephone.  Wi+h  269  Illustrations.  12mo., 
cloth,  352  pp $1 .00 

HOPKINS,  N.  M.  Experimental  Electrochemistry,  Theoretically  and  Prac- 
tically Treated.  Profusely  illustrated  with  130  new  drawings,  diagrams, 
and  photographs,  accompanied  by  a  Bibliography.  Illustrated. 
8vo.,  cloth,  29S  pp Net,  $3 . 00 

HOUSTON,  EDWIN  J.     A  Dictionary  of  Electrical  Words,  Terms,  and 

Phrases.     Fourth  Edition,  rewritten  and  greatly  enlarged.      582  Illus- 

.    trations.     4to.,  cloth Net,  $7 . 00 

A  Pocket  Dictionary  of  Electrical  Words,  Terms,  and  Phrases.  12mo., 
cloth,  950  pp Net,  $2 .50 

HUTCHINSON,  R.  W.,  Jr.  Long-Distance  Electric  Power  Transmission: 
Being  a  Treatise  on  the  Hydro-Electric  Generation  of  Energy;  Its 
Transformation,  Transmission,  and  Distribution.  Second  Edition. 
Illustrated.  12mo.,  cloth,  350  pp Net,  $3 .00 

-  and  IHLSENG,  M.  C.  Electricity  in  Mining.  Being  a  theoretical 
and  practical  treatise  on  the  construction,  operation,  and  mainte- 
nance of  electrical  mining  machinery.  12mo.,  cloth In  Press 

INCANDESCENT  ELECTRIC  LIGHTING.  A  Practical  Description  of 
the  Edison  System,  by  H.  Latimer.  To  which  is  added:  The  Design 
and  Operation  of  Incandescent  Stations,  by  C.  J.  Field;  A  Descrip- 
tion of  the  Edison  Electrolyte  Meter,  by  A.  E.  Kennelly;  and  a 
Paper  on  the  Maximum  Efficiency  of  Incandescent  Lamps,  by  T.  W. 
Howell.  Fifth  Edition.  Illustrated.  16mo.,  cloth,  140  pp.  (No. 
57  Van  Nostrand's  Science  Series.) 50  cents 

INDUCTION  COILS:  How  Made  and  How  Used.  Eleventh  Edition. 
Illustrated.  16mo.,  cloth,  123  pp.  (No.  53  Van  Nostrand's  Science 
Series.) 50  cents 

JEHL,  FRANCIS,  Member  A.I.E.E.  The  Manufacture  of  Carbons  for 
Electric  Lighting  and  other  purposes.  Illustrated  with  numerous 
Diagrams,  Tables,  and  Folding  Plates.  8vo.,  cloth,  232  pp .  .  Net,  $4 . 00 


JONES,  HARRY  C.  The  Electrical  Nature  of  Matter  and  Radioactivity. 
12mo.,  cloth,  212  pp $2.00 

KAPP,  GISBERT.  Electric  Transmission  of  Energy  and  its  Transforma- 
tion, Subdivision,  and  Distribution.  A  Practical  Handbook.  Fourth 
Edition,  thoroughly  revised.  Illustrated .  1 2mo . ,  cloth,  445  pp .  .  $3 . 50 

Alternate-Current  Machinery.  Illustrated.  16mo.,  cloth,  190  pp.  (No. 
96  Van  Nostrand's  Science  Series.) 50  cents 

Dynamos,  Alternators  and  Transformers.  Illustrated.  8vo.,  cloth,  507 
pp $4.00 

KELSEY,  W.  R.  Continuous-Current  Dynamos  and  Motors,  and  their 
Control;  being  a  series  of  articles  reprinted  from  the  "Practical 
Engineer,"  and  completed  by  W.  R.  Kelsey,  B.Sc.  With  Tables, 
Figures,  and  Diagrams.  8vo.,  cloth,  439  pp $2 .50 

KEMPE,  H.  R.  A  Handbook  of  Electrical  Testing.  Seventh  Edition, 
revised  and  enlarged.  Illustrated.  8vo.,  cloth,  706  pp. .  .Net,  $6.00 

KENNEDY,   R.     Modern   Engines   and   Power   Generators.     Illustrated. 

8vo.,  cloth,  5  vols.     Each $3 .50 

Electrical  Installations  of  Electric  Light,  Power,  and  Traction  Machinery. 
Illustrated.  8vo.,  cloth,  5  vols.  Each " $3 . 50 

KENNELLY,  A.  E.  Theoretical  Elements  of  Electro-Dynamic  Machinery. 
Vol.  I.  Illustrated.  8vo.,  cloth,  90  pp $1  .50 

KERSHAW,  J.  B.  C.     The  Electric  Furnace  in  Iron  and  Steel  Production. 

Illustrated.     8vo.,  cloth,  74  pp Net,  $1 .50 

Electrometallurgy.  Illustrated.  8vo.,  cloth,  303  pp.  (Van  Nos- 
trand's Westminster  Series.) Net.  $2 .00 

KINZBRUNNER,  C.     Continuous-Current  Armatures ;    their  Winding  and 

Construction.     79  Illustrations.     8vo.,  cloth,  80  pp Net,  $1  .50 

Alternate-Current  Windings;  their  Theory  and  Construction.  89  Illus- 
trations. 8vo.,  cloth,  80  pp Net,  $1  . 50 

KOESTER,  FRANK.  Steam-Electric  Power  Plants.  A  practical  treatise 
on  the  design  of  central  light  and  power  stations  and  their  econom- 
ical construction  and  operation.  Fully  Illustrated.  4to.,  cloth, 
455  pp N€t,  $5.00 

LARNER,  E.  T.  The  Principles  of  Alternating  Currents  for  Students  of 
Electrical  Engineering.  Illustrated  with  Diagrams.  12mo.,  cloth, 
144  pp ". .  .Net,  $1 .50 


LEMSTROM,  S.  Electricity  in  Agriculture  and  Horticulture.  Illustrated. 
8vo.,  cloth Net,  $1  .50 

LIVERMORE,  V.  P.,  and  WILLIAMS,  J.  How  to  Become  a  Competent 
Motorman  :  Being  a  practical  treatise  on  the  proper  method  of  oper- 
ating a  street-railway  motor-car;  also  giving  details  how  to  over- 
come certain  defects.  Second  Edition.  Illustrated.  16mo.,  cloth, 
247  pp Net,  $1 .00 

LOCKWOOD,  T.  D.     Electricity,  Magnetism,  and  Electro-Telegraphy.     A 

Practical  Guide  and  Handbook  of  General  Information  for  Electri- 
cal Students,  Operators,  and  Inspectors.  Fourth  Edition.  Illus- 
trated. 8vo.,  cloth,  374  pp $2 . 50 

LODGE,  OLIVER  J.  Signalling  Across  Space  Without  Wires:  Being  a 
description  of  the  work  of  Hertz  and  his  successors.  Third  Edition. 
Illustrated.  8vo.,  cloth Net,  $2 .00 

LORING,  A.  E.  A  Handbook  of  the  Electro-Magnetic  Telegraph. 
Fourth  Edition,  revised.  Illustrated.  16mo.,  cloth,  116  pp.  (No. 
39  Van  Nostrand's  Science  Series.) 50  cents 

LUPTON,  A.,  PARR,  G.  D.  A.,  and  PERKIN,  H.  Electricity  Applied  to 
Mining.  Second  Edition.  With  Tables,  Diagrams,  and  Folding 
Plates.  8vo.,  cloth,  320  pp. Net,  $4.50 

MAILLOUX,  C.  0.  Electric  Traction  Machinery.  Illustrated.  8vo., 
cloth In  Press 

MANSFIELD,  A.  N.  Electromagnets:  Their  Design  and  Construction. 
Second  Edition.  Illustrated.  16mo.,  cloth,  155  pp.  (No.  64.  Van 
Nostrand's  Science  Series.) 50  cents 

MASSIE,  W.  W.,  and  UNDERBILL,  C.  R.  Wireless  Telegraphy  and 
Telephony  Popularly  Explained.  With  a  chapter  by  Nikola  Tesla. 
Illustrated.  12mo.;  cloth,  82  pp Net,  $1 . 00 

MAURICE,  W.  Electrical  Blasting  Apparatus  and  Explosives,  with 
special  reference  to  colliery  practice.  Illustrated.  8vo.,  cloth, 
167  pp Net,  $3.50 

MAVER,  WM.,  Jr.  American  Telegraphy  and  Encyclopedia  of  the  Tele- 
graph Systems,  Apparatus,  Operations.  Fifth  Edition,  revised.  450 
Illustrations.  8vo.,  cloth,  656  pp Net,  $5 .00 


MONCKTON,  C.  C.  F.  Radio  Telegraphy.  173  Illustrations.  8vo., 
cloth,  272  pp.  (Van  Nostrand's  Westminster  Series.) Net,  $2 .00 

MUNRO,  J.,  and  JAMIESON,  A.  A  Pocket-Book  of  Electrical  Rules  and 
Tables  for  the  Use  of  Electricians,  Engineers,  and  Electrometallurgists. 
Eighteenth  Revised  Edition.  32mo.,  leather,  735  pp $2.50 

NIPHER.  FRANCIS  E.  Theory  of  Magnetic  Measurements.  With  an 
Appendix  on  the  Method  of  Least  Squares.  Illustrated.  12mo., 
cloth,  94  pp $1 .00 

NOLL,  AUGUSTUS.  How  to  Wire  Buildings.  A  Manual  of  the  Art  of 
Interior  Wiring.  Fourth  Edition.  Illustrated.  12mo.,  cloth, 
165  pp $1 . 50 

OHM,  G.  S.  The  Galvanic  Circuit  Investigated  Mathematically.  Berlin, 
1827.  Translated  by  William  Francis.  With  Preface  and  Notes 
by  Thos.  D.  Lockwood.  Second  Edition.  Illustrated.  16mo.,  cloth, 
269  pp.  (No.  102  Van  Nostrand's  Science  Series.) 50  cents 

OUDIN,  MAURICE  A.  Standard  Polyphase  Apparatus  and  Systems. 
Fifth  Edition,  revised.  Illustrated  with  many  Photo-reproductions, 
Diagrams,  and  Tables.  8vo.,  cloth,  369  pp Net,  $3 .00 

PALAZ,  A.  Treatise  on  Industrial  Photometry.  Specially  applied  to 
Electric  Lighting.  Translated  from  the  French  by  G.  W.  Patterson, 
Jr.,  and  M.  R.  Patterson.  Second  Edition.  Fully  Illustrated. 
8vo.,  cloth,  324  pp $4.00 

PARR,  G.  D.  A.  Electrical  Engineering  Measuring  Instruments  for  Com- 
mercial and  Laboratory  Purposes.  With  370  Diagrams  and  Engrav- 
ings. 8vo.,  cloth,  328  pp Net,  $3.50 

PARSHALL,  H.  F.,  and  HOBART,  H.  M.  Armature  Windings  of  Electric 
Machines.  Third  Edition.  With  140  full-page  Plates,  65  Tables, 
and  165  pages  of  descriptive  letter-press.  4to.,  cloth,  300  pp.  .$7.50 

Electric  Railway  Engineering.  With  437  Figures  and  Diagrams 
and  many  Table's.  4to.,  cloth,  475  pp Net,  $10 . 00 

Electric  Machine  Design.  Being  a  revised  and  enlarged  edition  of 
"Electric  Generators."  648  Illustrations.  4to.,  half  morocco,  601 
pp Net,  $12.50 


PERRINE,  F.  A.  C.  Conductors  for  Electrical  Distribution :  Their  Manu- 
facture and  Materials,  the  Calculation  of  Circuits,  Pole-Line  Construc- 
tion, Underground  Working,  and  other  Uses.  Second  Edition.  Illus- 
trated. 8vo.,  cloth,  287  pp Net,  $3.50 

POOLE,  C.  P.  The  Wiring  Handbook  with  Complete  Labor-saving  Tables 
and  Digest  of  Underwriters'  Rules.  Illustrated.  12mo.,  leather, 
85  pp Net,  $1  .00 

POPE,  F.  L.  Modern  Practice  of  the  Electric  Telegraph.  A  Handbook 
for  Electricians  and  Operators.  Seventeenth  Edition.  Illustrated. 
8vo.,  cloth,  234  pp $1 .50 

RAPHAEL,  F.  C.  Localization  of  Faults  in  Electric  Light  Mains.  Second 
Edition,  revised.  Illustrated.  8vo.,  cloth,  205  pp Net,  $3.00 

RAYMOND,  E.  B.  Alternating-Current  Engineering,  Practically  Treated. 
Third  Edition,  revised.  With  many  Figures  and  Diagrams.  8vo., 
cloth,  244  pp Net,  $2.50 

RICHARDSON,  S.  S.  Magnetism  and  Electricity  and  the  Principles  of  Elec- 
trical Measurement.  Illustrated.  12mo.,  cloth,  596  pp.  .Net,  $2.00 

ROBERTS,  J.  Laboratory  Work  in  Electrical  Engineering — Preliminary 
Grade.  A  series  of  laboratory  experiments  for  first-  and  second-year 
students  in  electrical  engineering.  Illustrated  with  many  Diagrams. 
8vo.,  cloth,  218  pp Net,  $2.00 

ROLLINS,  W.  Notes  on  X-Light.  Printed  on  deckle  edge  Japan  paper. 
400  pp.  of  text,  152  full-page  plates.  8vo.,  cloth Net,  $7.50 

RUHMER,  ERNST.  Wireless  Telephony  in  Theory  and  Practice.  Trans- 
lated from  the  German  by  James  Erskine-Murray.  Illustrated. 
8vo.,  cloth,  224  pp Net,  $3.50 

RUSSELL,  A.  The  Theory  of  Electric  Cables  and  Networks.  71  Illus- 
trations. 8vo.,  cloth,  275  pp Net,  $3 . 00 

SALOMONS,  DAVID.     Electric-Light  Installations.     A  Practical  Hand- 
book.    Illustrated.     12mo.,  cloth. 
Vol.1.:    Management  of  Accumulators.     Ninth  Edition.     178  pp.  $2. 50 

Vol.11.:    Apparatus.     Seventh  Edition.     318  pp $2.25 

Vol.  III. :    Application.     Seventh  Edition.     234  pp .- .  $1 . 50 


SCHELLEN,  H.  Magneto-Electric  and  Dynamo-Electric  Machines.  Their 
Construction  and  Practical  Application  to  Electric  Lighting  and  the 
Transmission  of  Power.  Translated  from  the  Third  German  Edition 
by  N.  S.  Keith  and  Percy  Neymann.  With  Additions  and  Notes 
relating  to  American  Machines,  by  N.  S.  Keith.  Vol.  I.  With 
353  Illustrations.  Third  Edition.  8vo.,  cloth,  518  pp $5.00 

SEVER,  G.  F.  Electrical  Engineering  Experiments  and  Tests  on  Direct- 
Current  Machinery.  Second  Edition,  enlarged.  With  Diagrams  and 
Figures.  8vo.,  pamphlet,  75  pp Net,  $1 .00 

and  TOWNSEND,  F.     Laboratory  and  Factory  Tests  in  Electrical 

Engineering.    Second  Edition,  revised  and  enlarged.    Illustrated.    8vo., 
cloth,  269  pp Net,  $2 . 50 

SEWALL,  C.  H.  Wireless  Telegraphy.  With  Diagrams  and  Figures. 
Second  Edition,  corrected.  Illustrated .  8vo . ,  cloth,  229  pp .  .  Net,  $2 . 00 

Lessons  in  Telegraphy.     Illustrated.     12mo.,  cloth,  104  pp.  .Net,  $1 .00 

—  T.     Elements    of    Electrical    Engineering.     Third  Edition,    revised. 
Illustrated.     8vo.,  cloth,  444  pp $3.00 

The  Construction  of  Dynamos  (Alternating  and  Direct  Current).  A 
Text-book  for  students,  engineering  contractors,  and  electricians-in- 
charge.  Illustrated.  8vo.,  cloth,  316  pp $3 .00 

SHAW,  P.  E.  A  First-Year  Course  of  Practical  Magnetism  and  Electricity. 
Specially  adapted  to  the  wants  of  technical  students.  Illustrated. 
8vo.,  cloth,  66  pp.  interleaved  for  note  taking Net,  $1 .00 

SHELDON,  S.,  and  MASON,  H.  Dynamo-Electric  Machinery:  Its  Con- 
struction, Design,  and  Operation. 

Vol.  I.:  Direct-Current  Machines.  Seventh  Edition,  revised.  Illus- 
trated. 8vo.,  cloth,  281  pp Net,  $2 .50 

and  HAUSMANN,  E.     Alternating-Current  Machines :    Being  the  sec- 
ond   volume    of    "Dynamo-Electric    Machinery;    its    Construction, 
•  Design,  and  Operation."     With  many  Diagrams  and  Figures.     (Bind- 
ing   uniform    with    Volume    I.)     Seventh    Edition,   rewritten.     8vo., 
cloth,  353  pp Net,  $2 . 50 

SLOANE,  T.  O'CONOR.  Standard  Electrical  Dictionary.  300  Illustra- 
tions. 12mo.,  cloth,  682  pp $3 .00 

Elementary  Electrical  Calculations.  How  Made  and  Applied.  Illus- 
trated. 8vo.,  cloth,  300  pp In  Press 


SNELL,  ALBION  T.  Electric  Motive  Power.  The  Transmission  and  Dis- 
tribution of  Electric  Power  by  Continuous  and  Alternating  Currents. 
With  a  Section  on  the  Applications  of  Electricity  to  Mining  Work. 
Second  Edition.  Illustrated.  8vo.,  cloth,  411  pp Net,  $4 .00 

SODDY,  F.  Radio-Activity ;  an  Elementary  Treatise  from  the  Stand- 
point of  the  Disintegration  Theory.  Fully  Illustrated.  8vo.,  cloth, 
214  pp Net,  $3.00 

SOLOMON,  MAURICE.  Electric  Lamps.  Illustrated.  8vo.,  cloth.  (Van 
Nostrand's  Westminster  Series.) Net,  $2 . 00 

STEWART,  A.  Modern  Polyphase  Machinery.  Illustrated.  12mo., 
cloth,  296  pp Net,  $2 .00 

SWINBURNE,  JAS.,  and  WORDINGHAM,  C.  H.  The  Measurement  of 
Electric  Currents.  Electrical  Measuring  Instruments.  Meters  for 
Electrical  Energy.  Edited,  with  Preface,  by  T.  Commerford  Martin. 
Folding  Plate  and  Numerous  Illustrations.  16mo,,  cloth,  241  pp. 
(No.  109  Van  Nostrand's  Science  Series.) 50  cents 

SWOOPE,  C.  WALTON.  Lessons  in  Practical  Electricity:  Principles, 
Experiments,  and  Arithmetical  Problems.  An  Elementary  Text- 
book. With  numerous  Tables,  Formulae,  and  two  large  Instruction 
Plates.  Ninth  Edition.  Illustrated.  8vo.,  cloth,  462  pp .  Net,  $2 . 00 

THOM,  C.,  and  JONES,  W.  H.  Telegraphic  Connections,  embracing  recent 
methods  in  Quadruplex  Telegraphy.  20  Colored  Plates.  8vo., 
cloth,  59  pp $1 .50 

THOMPSON,  S.  P.,  Prof.  Dynamo-Electric  Machinery.  With  an  Intro- 
duction and  Notes  by  Frank  L.  Pope  and  H.  R.  Butler.  Fully  Illus- 
trated. 16mo.,  cloth,  214  pp.  (No.  66  Van  Nostrand's  Science 
Series.) 50  cents 

Recent  Progress  in  Dynamo-Electric  Machines.  Being  a  Supplement  -to 
"Dynamo-Electric  Machinery."  Illustrated.  16mo.,  cloth,  113  pp. 
(No.  75  Van  Nostrand's  Science  Series.) 50  cents 

TOWNSEND,  FITZHUGH.  Alternating  Current  Engineering.  Illus- 
trated. 8vo.,  paper,  32  pp Net,  75  cents 

UNDERBILL,  C.  R.  The  Electromagnet:  Being  a  new  and  revised  edi- 
tion of  "  The  Electromagnet,"  by  Townsend  Walcott,  A.  E.  Kennelly, 
and  Richard  Varley.  W7ith  Tables  and  Numerous  Figures  and  Dia- 
grams. 12mo  ,  cloth New  Revised  Edition  in  Press 


URQUHART,  J.  W.  Dynamo  Construction.  A  Practical  Handbook  for 
the  use  of  Engineer  Constructors  and  Electricians  in  Charge.  Illus- 
trated. 12mo.,  cloth -. .  .$3.00 

Electric  Ship-Lighting.  A  Handbook  on  the  Practical  Fitting  and  Run- 
ning of  Ship's  Electrical  Plant,  for  the  use  of  Ship  Owners  and  Build  - 
eis,  Marine  Electricians,  and  Sea-going  Engineers  in  Charge.  88 
Illustrations.  12mo.,  cloth,  303  pp $3 .00 

Electric-Light  Fitting.  A  Handbook  for  Working  Electrical  Engineers, 
embodying  Practical  Notes  on  Installation  Management.  Second 
Edition,  with  additional  chapters.  With  numerous  Illustrations. 
12mo.,  cloth $2.00 

Electroplating.  A  Practical  Handbook.  Fifth  Edition.  Illustrated. 
12mo.,  cloth,  230  pp $2.00 

Electrotyping.     Illustrated.     12mo.,  cloth,  228  pp $2 .00 

WADE,  E.  J.  Secondary  Batteries:  Their  Theory,  Construction,  and  Use. 
With  innumerable  Diagrams  and  Figures.  8vo.,  cloth.  New  Edition 

in  Press 

WALKER,  FREDERICK.  Practical  Dynamo-Building  for  Amateurs. 
How  to  Wind  for  any  Output.  Third  Edition.  Illustrated.  16mo., 
cloth,  104  pp.  (No.  98  Van  Nostrand's  Science  Series.) 50  cents 

-  SYDNEY  F.  Electricity  in  Homes  and  Workshops.  A  Practical 
Treatise  on  Auxiliary  Electrical  Apparatus.  Fourth  Edition.  Illus- 
trated. 12mo.,  cloth,  358  pp $2 .00 

Electricity  in  Mining.     Illustrated.     8vo.,  cloth,  385  pp . . .$3.50 

WALLING,  B.  T.,  Lieut.-Com.  U.S.N.,  and  MARTIN,  JULIUS.  Electrical 
Installations  of  the  United  States  Navy.  With  many  Diagrams  and 
Engravings.  8vo.,  cloth,  648  pp $6 .00 

WALMSLEY,  R.  M.  Electricity  in  the  Service  of  Man.  A  Popular  and 
Practical  Treatise  on  the  Application  of  Electricity  in  Modern  Life. 
Illustrated.  8vo.,  cloth,  1208  pp Net,  $4.50 

WATT,  ALEXANDER.  Electroplating  and  Refining  of  Metals.  New 
Edition,  rewritten  by  Arnold  Philip.  Illustrated.  8vo.,  cloth,  677 
pp Net,  $4.50 

Electrometallurgy.  Fifteenth  Edition.  Illustrated.  12mo.,  cloth,  225 
pp $1 .00 


WEBB,  H.  L.  A  Practical  Guide  to  the  Testing  of  Insulated  Wires  and 
Cables.  Fifth  Edition.  Illustrated .  12mo.,  cloth,  1 18  pp $1 . 00 

WEEKS,  R.  W.      The  Design  of  Alternate-Current  Transformer. 

New  Edition  in  Press 

WEYMOUTH,  F.  MARTEN.  Drum  Armatures  and  Commutators. 
(Theory  and  Practice.)  A  complete  treatise  on  the  theory  and  con- 
struction of  drum-winding,  and  of  commutators  for  closed-coil  arma- 
tures, together  with  a  full  resume  of  some  of  the  principal  points 
involved  in  their  design,  and  an  exposition  of  armature  reactions 
and  sparking.  Illustrated.  8vo.,  cloth,  295  pp Net,  $3.0C 

WILKINSON,  H.  D.  Submarine  Cable-Laying,  Repairing,  and  Testing. 
New  Edition.  Illustrated.  8vo.,  cloth In  Press 

YOUNG,  J.  ELTON.  Electrical  Testing  for  Telegraph  Engineers.  Illus- 
trated. 8vo.,  cloth,  264  pp Net,  $4 .00 

A  112=page  Catalog  of  Books  on  Electricity,  classified  by 
subjects,  will  be  furnished  gratis,  postage  prepaid, 
on  application. 


Seventh  Edition,  New  and  Entirely  Revised 
8vo,  Cloth       355  Pages       236  Illustrations       $2.50  Net 

Alternating-  Current 
Machines 

Being  the  Second  Volume  of 

Dynamo  Electric  Machinery 

Its  Construction,  Design 
and  Operation 

Samuel  Sheldon,  A.M.,Ph.D.,D.Sc. 

Prof,  of  Physics  and  Elec.  Engineering,  Polytechnic  Inst.,  Brooklyn 

AND 

Hobart  Mason,  B.S.,E.R 

AND 

Erich  Hausmann,  B.S.,-E.E. 


BOOK  has  been  entirely  re-written  to  bring  it  into  accord 
I  with  the  present  conditions  of  practice.  It  contains  one-third  more 
material  than  the  first  edition,  two-thirds  of  which  is  new  matter. 
It  is  intended  for  use  as  a  text-book  in  technical  schools  and  colleges  for 
students  pursuing  either  electrical  or  non-electrical  engineering  courses. 
It  is  so  arranged  that  portions  may  be  readily  omitted  in  the  case  of  the 
latter  without  affecting  the  correlation  of  the  remaining  parts.  The  new 
matter  contains  numerous  problems,  rigid  derivations  of  the  fundamental 
laws  of  alternating  current  circuits,  vector  diagrams  pertaining  to  the  cir- 
cuits of  alternating  current  machines,  methods  of  determining  from  tests 
the  behavior  of  machines  and  of  predetermining  their  behaviour  from 
design  data.  There  is  also  given  a  method  of  calculating  all  the  leakage 
fluxes  of  the  induction  motor.  The  last  chapter  gives  complete  directions 
for  the  design  and  construction  of  transmission  lines  in  accordance  with 
modem  practice.  _  _  _ 

D.  VAN  NOSTRAND  COMPANY 

Publishers  and  Booksellers 
23    Murray   and    27   "Warren  Streets  New  YorR 


THE  NEW  FOSTER 

Fifth  Edition,  Completely  Revised  and  Enlarged,  with  Four- 
fifths  of  Old  Matter  replaced  by  New,  Up-to-date  Material. 
Pocket  size,  flexible  leather,  elaborately  illustrated,  with  an  ex- 
tensive index,  1  636  pp.,  Thumb  Index,  etc.  Price,  $5.00 

Electrical  Engineer's  Pocketbook 

The  Most  Complete  Book  of  Its  Kind  Ever  Published, 

Treating  of  the  Latest  and  Best  Practice 

in  Electrical  Engineering 

By  Horatio  A.  Foster 

Member  Am.  Inst.  E.  E.,  Member  Am.  Soc.  M.  E. 

With  the  Collaboration  of  Eminent  Specialists 

CONTENTS 

Symbols,  Units,  Instruments 
M  easurements 
Magnetic  Properties  of  Iron 
Blectro  Magnets 
Properties  of  Conductors 
Relations  and  Dimensions  of  Con- 
ductors 

Underground  Conduit  Construction 
Standard  Symbols 
Cable  Testing 
Dynamos  and  Motors 
Tests  of  Dynamos  and  Motors 
The  Static  Transformer 
Standardization  Rules 
Illuminating  Engineering 
Electric  lighting  (Arc) 
Electric lyigh ting  (Incandescent) 
Electric  Street  Railways 
Electrolysis 
Transmission  of  Power 
Storage  Batteries 
Switchboards 
I/ghtning  Arresters 
Electricity  Meters 
Wireless  Telegraphy 
Telegraphy 
Telephony 

Electricity  in  the  U.  S.  Army 
Electricity  in  the  U.  S.  Navy 
Resonance 

Electric  Automobiles          X-Rays                                         lightning  Conductors 
Electro-chemistry  and        Electric  Heating,  Cooking       Mechanical  Section 
Electro-metallurgy  and  Welding Index 

D.  VAN    NOSTRAND    COMPANY 

23  MURRAY  and  27  WARREN  STREETS         NEW  YORK 


RETURN 
TO—  * 

ENGINEERING  LIBRARY 

642-3366 

LOAN  PERIOD  1 

2 

3 

4 

5 

6 

ALL  BOOKS  MAY  BE  RECALLED  AFTER  7  DAYS 
Overdues  subject  to  replacement  charges 


DUE  AS  STAMPED  BELOW 

MONOGRAPH 

JUN43J980 

lamstHttmi 

FEB  0  4  Z0° 

SENT  ON  ILL 

MAY  1  6  2006 

U.C.  BERKELEY 

UNIVERSITY  OF  CALIFORNIA,  BERKELEY 
FORM  NO.  DD11,  10m,  11/78       BERKELEY,  CA  94720 


V 

Bngineerinf 
Library 


2103 


